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Challenging local realism with human choices
†The BIG Bell Test Collaboration: C. Abell´an,1A. Ac´ın,1, 2 A. Alarc´on,3,4 O. Alibart,5C. K. Andersen,6F. Andreoli,7A.
Beckert,6F. A. Beduini,1A. Bendersky,8M. Bentivegna,7P. Bierhorst,9D. Burchardt,10 A. Cabello,11 J. Cari˜ne,3, 4, 12 S.
Carrasco,1G. Carvacho,7D. Cavalcanti,1R. Chaves,13 J. Cort´es-Vega,3,12 A. Cuevas,7A. Delgado,3, 12 H. de Riedmatten,1, 2
C. Eichler,6P. Farrera,1J. Fuenzalida,3, 12, 14 M. Garc´ıa-Matos,1R. Garthoff,10 S. Gasparinetti,6T. Gerrits,9F. Ghafari
Jouneghani,15, 16 S. Glancy,9E. S. G´omez,3, 12 P. Gonz´alez,3, 12 J.-Y. Guan,17, 18 J. Handsteiner,14, 19 J. Heinsoo,6G. Heinze,1
A. Hirschmann,1O. Jim´enez,1F. Kaiser,5E. Knill,9L. T. Knoll,20, 21 S. Krinner,6P. Kurpiers,6M. A. Larotonda,20, 21 J.-˚
A.
Larsson,22 A. Lenhard,1H. Li,23,24 M.-H. Li,17, 18 G. Lima,3, 12 B. Liu,25, 14 Y. Liu,17, 18 I. H. L´opez Grande,20, 21 T. Lunghi,5
X. Ma,26 O. S. Maga˜na-Loaiza,9P. Magnard,6A. Magnoni,21 M. Mart´ı-Prieto,1D. Mart´ınez,3, 12 P. Mataloni,7A.
Mattar,1M. Mazzera,1R. P. Mirin,9M. W. Mitchell,1, 2, ∗S. Nam,9M. Oppliger,6J.-W. Pan,17, 18 R. B. Patel,15, 16 G. J.
Pryde,15, 16 D. Rauch,14, 19 K. Redeker,10 D. Riel¨ander,1M. Ringbauer,27,28 T. Roberson,27, 28 W. Rosenfeld,10 Y.
Salath´e,6L. Santodonato,7G. Sauder,5T. Scheidl,14, 19 C. T. Schmiegelow,21 F. Sciarrino,7A. Seri,1L. K. Shalm,9
S.-C. Shi,29 S. Slussarenko,15,16 M. J. Stevens,9S. Tanzilli,5F. Toledo,3, 12 J. Tura,1, 30 R. Ursin,14, 19 P. Vergyris,5V.
B. Verma,9T. Walter,6A. Wallraff,6Z. Wang,23, 24 H. Weinfurter,10, 30 M. M. Weston,15, 16 A. G. White,27, 28 C.
Wu,17, 18 G. B. Xavier,3, 4, 22 L. You,23, 24 X. Yuan,26 A. Zeilinger,14, 19 Q. Zhang,17, 18 W. Zhang,23, 24 and J. Zhong29
1ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
2ICREA – Instituci´o Catalana de Recerca i Estudis Avan¸cats, 08010 Barcelona, Spain
3Millennium Institute for Research in Optics, Universidad de Concepci´on, 160-C Concepci´on, Chile
4Departamento de Ingenier´ıa El´ectrica, Universidad de Concepci´on,160-C Concepci´on, Chile
5Universit´e Cˆote d’Azur, CNRS UMR 7010, Insitut de Physique de Nice (INPHYNI), Parc Valrose, 06108 Nice Cedex 2, France
6Department of Physics, ETH Zurich, CH-8093 Zurich, Switzerland
7Dipartimento di Fisica, Sapienza Universit`a di Roma, I-00185 Roma, Italy
8Departamento de Computaci´on, FCEyN, UBA and ICC, CONICET, Pabell´on 1, Ciudad Universitaria, 1428 Buenos Aires, Argentina
9National Institute of Standards and Technology, 325 Broadway, Boulder, CO 80305, USA
10Ludwig-Maximilians-Universit¨at, 80799 M¨unchen, Germany
11Departamento de F´ısica Aplicada II, Universidad de Sevilla, 41012 Sevilla, Spain
12Departamento de F´ısica, Universidad de Concepci´on, 160-C Concepci´on, Chile
13International Institute of Physics, Federal University of Rio Grande do Norte, 59070-405 Natal, Brazil
14Institute for Quantum Optics and Quantum Information (IQOQI),
Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
15Centre for Quantum Computation and Communication Technology, Griffith University, Brisbane, Queensland 4111, Australia
16Centre for Quantum Dynamics, Griffith University, Brisbane, Queensland 4111, Australia
17Shanghai Branch, National Laboratory for Physical Sciences at Microscale and Dept. of
Modern Physics, University of Science and Technology of China, Shanghai 230026, China
18Shanghai Branch, CAS Center for Excellence and Synergetic Innovation Center in Quantum Information
and Quantum Physics, University of Science and Technology of China, Shanghai 230026, China
19Vienna Center for Quantum Science & Technology (VCQ), Faculty of Physics, University of Vienna, Vienna, Austria
20DEILAP, CITEDEF & CONICET, J.B. de La Salle 4397, 1603 Villa Martelli, Buenos Aires, Argentina
21Departamento de F´ısica, FCEyN, UBA and IFIBA, Conicet, Pabell´on 1, Ciudad Universitaria, 1428 Buenos Aires, Argentina
22Department of Electrical Engineering, Link¨oping University, 581 83 Link¨oping, Sweden
23State Key Laboratory of Functional Materials for Informatics, Shanghai Institute of
Microsystem and Information Technology, Chinese Academy of Sciences, Shanghai 200050, China
24CAS Center for Excellence in Superconducting Electronics, Shanghai 200050, China
25School of Computer, NUDT, 410073 Changsha, China
26Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
27Centre for Engineered Quantum Systems, University of Queensland, Brisbane, Queensland 4072, Australia
28School of Mathematics and Physics, University of Queensland, Brisbane, Queensland 4072, Australia
29Purple Mountain Observatory and Key Laboratory of Radio Astronomy,
Chinese Academy of Sciences, 2 West Beijing Road, Nanjing 210008, China
30Max-Planck-Institut f¨ur Quantenoptik, Hans-Kopfermann-Strasse 1, Garching 85748, Germany
(Dated: May 22, 2018)
∗morgan.mitchell@icfo.eu
arXiv:1805.04431v2 [quant-ph] 20 May 2018
1
Challenging local realism with human choices
The BIG Bell Test Collaboration†
A Bell test, which challenges the philosophical worldview
of local realism1against experimental observations, is
a randomized trial requiring spatially-distributed entan-
glement, fast and high-efficiency detection, and unpre-
dictable measurement settings2,3. While technology can
perfect the first two of these4–7, and while technolog-
ical randomness sources8,9 enable “device-independent”
protocols based on Bell inequality violation10,11, challeng-
ing local realism using physical randomizers inevitably
makes assumptions about the same physics one aims to
test. Bell himself noted this weakness of physical setting
choices and argued that human “free will” could rigor-
ously be used to assure unpredictability in Bell tests12.
Here we report a suite of local realism tests using human
choices, avoiding such assumptions about predictability
in physics. We recruited ≈100,000 human participants
to play an online video game that incentivizes fast, sus-
tained input of unpredictable bits while also illustrat-
ing Bell test methodology13. The participants gener-
ated 97,347,490 binary choices, which were directed via
a scalable web platform to twelve laboratories on five
continents, in which 13 experiments tested local real-
ism using photons5,6, single atoms7, atomic ensembles14 ,
and superconducting devices15. Over a 12-hour period
on the 30th of November 2016, participants worldwide
provided a sustained flow of over 1000 bits/s to the ex-
periments, which used different human-generated bits
to choose each measurement setting. The observed
correlations strongly contradict local realism and other
realist positions in bi-partite and tri-partite16 scenar-
ios. Project outcomes include closing of the freedom-of-
choice loophole17, gamification18 of statistical and quan-
tum non-locality concepts, new methods for quantum-
secured communications, a very large dataset of human-
generated randomness, and networking techniques for
global participation in experimental science.
Bell tests, like Darwin’s studies of finches and Galileo’s ob-
servations of the moons of Jupiter, bring empirical methods
to questions previously accessible only by other means, e.g.
by philosophy or theology19. Local realism, i.e., realism plus
relativistic limits on causation, was debated by Einstein and
Bohr using metaphysical arguments, and recently has been re-
jected by Bell tests4–7 that closed all technical “loopholes.”
Recent work on “device-independent” quantum information10
shows how Bell inequality violation (BIV) can also challenge
causal determinism20, a second topic formerly accessible only
by metaphysics21. Central to both applications is the use of free
variables to choose measurements: in the words of Aaronson22
“Assuming no preferred reference frames or closed timelike
curves, if Alice and Bob have genuine ‘freedom’ in deciding
how to measure entangled particles, then the particles must
also have ‘freedom’ in deciding how to respond to the measure-
ments.” Provable indeterminism is useful in communications
security11.
Prior Bell tests used physical devices8,9 to “decide” for Al-
ice and Bob, and thus demonstrated only a relation among
physical processes: if some processes are “free” in the required
sense (see Methods), then other processes are similarly “free.”
In the language of strong Bell tests, this conditional relation
leaves open the freedom-of-choice loophole (FoCL, see Meth-
ods): because we cannot guarantee such freedom within local
realism, the tests must assume physical indeterminacy in the
hidden-variable theory2. Laboratory methods can “tighten”
but never close this loophole2–6, motivating new approaches.
Gallicchio, Friedman, and Kaiser23 have proposed choosing
settings by observation of cosmic sources at the edge of the vis-
ible universe. A Bell inequality violation under such conditions
could only be explained within local realism if events across
all of history conspire to produce the measured outcomes24,25.
Bell himself argued that human choices could be considered
“free variables” in a Bell test12 (see Methods), and noted
the impracticality of using humans with 1970’s technologies.
Here we implement Bell’s idea, using modern crowd-sourcing,
networking, and gamification18 techniques. In this BIG Bell
Test (BBT) the “Alice” and “Bob” of Aaronson’s formulation
are real people. Assuming no faster-than-light communication,
such experiments can prove the conditional relation: if human
will is free, there are physical events with no causes.
It is perhaps surprising that human choices, which are known
to contain statistical regularities26, are sufficiently random for a
Bell test. Recent works on statistical analysis of Bell tests3,27,28
clarify this: provided statistical independence of settings and
hidden variables (see Methods), patterns do not strongly influ-
ence a BIV’s p-value. Statistical interdependence of settings
and hidden variables can arise due to hidden variables influenc-
ing the choices (FoCL), or vice versa (locality loophole = LL).
Patterns do strongly affect p-values in experiments that try to
close LL by space-like separation, as they allow current choices
to be predicted from earlier choices. As described later, the
BBT takes a different approach to LL.
A major obstacle to a Bell test with humans has been the
difficulty of generating enough choices for a statistically signif-
icant test. A person can generate roughly three random bits
per second, while a strong test may require millions of set-
ting choices in a time span of minutes to hours, depending on
the speed and stability of the experiment. To achieve such
rates, we crowd-sourced the basis choices, recruiting in total
about 100,000 participants, the Bellsters, over the course of
the project. Each choice by a participant, encoded as a bit,
‘0’ or ‘1’, was entered in an internet-connected device such as
the participant’s mobile phone. Servers collated the incoming
bits and streamed them live to the 13 experiments, see Fig. 1.
Each measurement was determined by distinct bits, reflecting
individual human choices. To encourage participants to con-
tribute a larger number of more unpredictable bits, the input
was collected in the context of a video game, “The BIG Bell
Quest,” implemented in javascript to run directly in a device’s
web browser.
“The BIG Bell Quest” is designed to reward sustained, high-
rate input of unpredictable bits, while also being engaging and
2
FIG. 1. Structure of The BIG Bell Test. a) human participants, or “Bellsters,” enter ‘0’s and ‘1’s in an online video game that
incentivizes sustained generation of unpredictable bits. b) experiments use Bellster-generated bits to control measurement-defining
elements, such as wave-plates for photons or microwave pulses for matter qubits. Shown is a micrograph of superconducting qubits
used in 7
, with the measured CHSH Bell parameter midway through the BBT day. c) A cloud-based networking system integrates
the activities a) and b), serving game elements to Bellsters, distributing input bits to connected laboratories, and providing in-game
feedback about experimental use of the player’s input. Through this system, Bellsters are given direct, if brief, control of the
experimental apparatus, so that each measurement setting is determined by a single human choice, traceable to a given user ID and
time of entry. See Methods.
informative. An interactive explanation first describes quan-
tum nonlocality and the role played by participants and exper-
imenters in the BBT. The player is then tasked with entering
a given number of unpredictable bits within a limited time. A
machine learning algorithm (MLA) attempts to predict each
input bit, modelling the user’s input as a Markov process and
updating the model parameters using reinforcement learning
(see Methods). Scoring and level completion reflect the degree
to which the MLA predicts the player’s input, motivating play-
ers to consider their own predictability and take conscious steps
to reduce it, but the MLA does not act as a filter: all input is
passed to the experiments. Bellster input showed unsurprising
deviations from ideal randomness26, e.g., P(0) ≈0.5237 (bias
toward ‘0’ ) while adjacent bits show P(01) + P(10) ≈0.6406
(excess of alternation).
Modern video-game elements were incorporated to boost
engagement (animation, sound), to encourage persistent play
(progressive levels, power-ups, boss battles, leaderboards) and
to recruit new players (group formation, posting to social net-
works). Different level scenarios illustrate key elements of the
BBT: human input, global networking, and measurements on
quantum systems, while boss battles against “oracles” con-
vey the conceptual challenge of unpredictability. Level com-
pletion is rewarded with 1) a report on how many bits from
that level were used in each experiment running at that time,
2) a “curious fact” about statistics, Bell tests, or the various
experiments, and, if the participant is lucky, 3) one of sev-
eral videos recorded in the participating laboratories, explain-
ing the experiments. The game and BBT website (preserved
at http://museum.thebigbelltest.org) are available in Chinese,
English, Spanish, French, German, Italian and Catalan, mak-
ing them accessible to roughly three billion first- and second-
language speakers.
To synchronize participant activity with experimental opera-
tion, the Bell tests were scheduled for a single day, Wednesday
30 November 2016. The date was chosen so that most schools
worldwide would be in session, and to avoid competing media
events such as the US presidential election. Participants were
recruited by a variety of channels, including traditional and so-
cial media and school and science museum outreach, with each
partner institution handling recruitment in their regions of fa-
miliarity. The media campaign focused on the nature of the
experiment and the need for human participants. The press
often communicated this with headlines such as “Quantum
theory needs your help” (China Daily). A first, small campaign
in early October was made to seed “viral” diffusion of the story
and a second, large campaign 29-30 November was made to
attract a wide participant base. The media campaign gener-
ated at least 230 headlines in printed and online press, radio
and television.
The data networking architecture of the BBT, shown in
Fig. 1, includes elements of instant messaging and online gam-
ing, and is designed to efficiently serve a fluctuating number
of users with orders-of-magnitude prior uncertainty. A gam-
ing component handles the BBT website, participant accounts
management, delivery of game code (javascript and video),
score records and leaderboards. In parallel, a messaging com-
ponent handles data conditioning, streaming to experiments,
and reporting of participant choices generated via the game.
Horizontal scaling is used in both components: participants
connect not directly to servers but rather to dynamic load
balancers that spread the input among a pool of servers dy-
namically scaled in response to load. Data arrival timing was
used for a honeypot strategy to identify robot “participants”
and remove their input from the data stream without alerting
their masters to the practice. A single, laboratory-side server
received data from the participant-side servers, concatenated
the user input and streamed it to the labs at laboratory-defined
rates. See Methods for details.
By global time zoning, November 30th defines a 51-hour
window, from 0:00 UTC+14h (e.g. Samoa) to 23:59 UTC-
12h (e.g. Midway island). Nevertheless, most participants
3
FIG. 2. Geography and timing of the BBT. a) Locations of the 13 BBT experiments, ordered from East to West. See Table
I. Shading shows total sessions by country. Eight sessions from Antarctica are not shown. b) Temporal evolution of the project.
(top) live sessions versus time for different continent groups, showing a strong drop-off in the local early morning in each region.
The spike in Asian participation around 11:00 UTC coincides with a live-streamed event in Barcelona, translated into Chinese and
re-streamed by USTC. (middle) number of connected labs versus time, divided into experiments using only photons and experiments
with at least one material component, e.g. atoms or superconductors. (bottom) input bitrate versus time. Data flow remains nearly
constant despite regional variations, with Asian Bellsters handing off to Bellsters from the Americas in the critical period 12:00-00:00
UTC. Session data from Google analytics.
contributed during a 24-hour window centred on 18:00 UTC.
Recruitment of participants was geographically uneven, with
a notable failure to recruit large numbers of participant from
Africa. Despite this, the latitude zones of Asia/Oceania, Eu-
rope/Africa, and the Americas had comparable participation,
which proved important for the experiment. As shown in Fig. 2,
input from any single region dropped to low values during the
local early morning, but was compensated by high input from
other regions, resulting in a high sustained global bit rate. Over
the 12-hour period from 09:00 UTC to 21:00 UTC, 30 Novem-
ber 2016, the input exceeded 103bits per second, allowing a
majority of the experiments to run at their full speed. Several
experiments posted their results live on social networks. Due
to its high speed, 13
accumulated human bits for several hours
and then used them in a few-minute acquisition. 9
had visi-
bility sufficient to show entanglement but not a BIV, although
a BIV was observed later with stored human bits.
The Earth is only 43 light-ms in diameter, so human choices
are too slow to be space-like separated from the measurements.
This leaves open LL as concerns choice-to-remote-detection in-
fluence. Influence between Alice and Bob’s measurements is
nonetheless excluded by timing in three BBT experiments. To
tighten LL, we take a strategy we call the BIG test: many simul-
taneous Bell tests in widely-separated locations using different
physical systems, with apparatuses constructed and operated
by different experimental teams. In this BIG test, a hidden-
variable theory can only exploit LL if it has mechanisms by
which the choices simultaneously influence hidden variables in
all of these experiments, bringing them each to a result mim-
icking quantum predictions.
The suite of 13 BBT experiments, including true Bell tests
and other realism tests requiring free choice of measurement,
are summarized in Table I and described in the Supplementary
Information. Experiments 1
,2
,3
,4
,5
,8
,11
,12
, and
13
used entangled photon pairs, 6
used single-photon/single-
atom entanglement, 9
used single-photon/atomic ensemble
entanglement, and 7
used entangled superconducting qubits.
Experiments 3
,8
and 13
achieved space-like separation
of Alice and Bob’s measurements. Experiments 7
and
13
used high-efficiency detection to avoid the fair sampling
assumption. 5
demonstrated a violation of bi-local realism,
while 10
violated a Bell inequality for multi-mode entangle-
ment. 1
demonstrated quantum steering and 2
demon-
strated entanglement in time with a three-station measure-
ment. 12
closed the post-selection loophole typically present
in Bell tests based on energy-time entanglement. Analysis of
3
puts bounds on how well a measurement-dependent local
model would have to predict Bellster behaviour to produce the
observed results29.3
,4
,6
and 13
tested for differences
between nonlocal correlations with human- versus machine-
4
TABLE I. Experiments carried out as part of the BBT, ordered by longitude, from East to West. Descriptions of the experiments
are given in Methods. “Stat. Sig.” (statistical significance) indicates number of standard deviations assuming i.i.d. trials, unless
otherwise indicated. γsignifies photon.
ID Lead Institution Location Entangled system Rate Inequality Result Stat. Sig.
1
GRIFFITH Brisbane, AU γpolarisation 4 bps S16 ≤0.511 S16 = 0.965 ±0.008 57 σ
2
EQUS Brisbane, AU γpolarisation 3 bps |S| ≤ 2SAB = 2.75 ±0.05
SBC = 2.79 ±0.05
15 σ
16 σ
3
USTC Shanghai, CN γpolarisation 1 kbps PRBLG29
Jl≥0
l0= 0.10 ±0.05
J1/4=−0.0181 ±0.0006
N/A
30 σ
4
IQOQI Vienna, AT γp olarisation 1.61 kbps |S| ≤ 2SHRN = 2.639 ±0.008
SQRN = 2.643 ±0.006
81 σ
116 σ
5
SAPIENZA Rome, IT γpolarisation 0.62 bps B≤1B= 1.225 ±0.007 32 σ
6
LMU Munich, DE γ-atom 1.7 bps |S| ≤ 2SHRN = 2.427 ±0.0223
SQRN = 2.413 ±0.0223
19 σ
18.5 σ
7
ETHZ Zurich, CH transmon qubit 3 kbps |S| ≤ 2S= 2.3066 ±0.0012 p<10−99
8
INPHYNI Nice, FR γtime-bin 2 kbps |S| ≤ 2S= 2.431 ±0.003 140 σ
9
ICFO Barcelona, ES γ-atom ensemble 125 bps |S| ≤ 2S= 2.29 ±0.10 2.9 σ
10
ICFO Barcelona, ES γmulti-frequency-bin 20 bps |S| ≤ 2S= 2.25 ±0.08 3.1 σ
11
CITEDEF Buenos Aires, AR γpolarisation 1.02 bps |S| ≤ 2S= 2.55 ±0.07 7.8 σ
12
CONCEPCION Concepcion, CL γtime-bin 51 kbps |S| ≤ 2S= 2.43 ±0.02 20 σ
13
NIST Boulder, US γpolarisation 100 kbps K≤0K= (1.65 ±0.20) ×10−48.7 σ
generated randomness. Most experiments observed statisti-
cally strong violations of their respective inequalities, justifying
rejection of local realism in a multitude of systems and scenar-
ios.
In summary, on 30 November 2016, a suite of 13 Bell tests
and similar experiments, using photons, single atoms, atomic
ensembles and superconducting devices, demonstrated strong
disagreement with local realism, using measurement settings
chosen by tens of thousands of globally-distributed human par-
ticipants. The results also show empirically that human agency
is incompatible with causal determinism20–22, a question for-
merly accessible only by metaphysics. The experiments reject
local realism in a variety of never-before-tested physical systems
and scenarios, set the groundwork for Bell-test based applica-
tions in quantum information, introduce the first gamification
of Bell tests and unpredictability concepts, and demonstrate
global networking techniques by which hundreds of thousands
of individuals can directly participate in experimental science.
Acknowledgements: We are deeply grateful to the many peo-
ple and organizations who contributed to this project, start-
ing with the fabulous Bellsters. We thank the Ministerio
de Educaci´on, Cultura y Deporte of Spain, INTEF, Optical
Society of America, Investigaci´on y Ci´encia,Big Van,Crea
Ci´encia, Politecnico di Milano, University of Waterloo / In-
stitute for Quantum Computing, Toptica, EPS Young Minds,
Real Sociedad Espa˜nola de F´ısica, Ajuntament de Barcelona,
Universit`a degli studi di Padova, Universit`a degli studi del
l’Insubria, CNRIFN Istituto di Fotonica e Nanotecnologia, Is-
tituto d’Istruzione Superiore Carlo Livi, Clara Grima, Esteban
Berm´udez, Alessandro Fedrizzi, Fabio Costa, Michael Goggin,
and Shakib Daryanoosh.
We acknowledge financial support from: CONICET and
ANPCyT (Argentina), ARC and UQ Centres for Engineered
Quantum Systems (CE110001013) and for Quantum Compu-
tation and Communication Technology (CE110001027), AGW
acknowledges UQ Vice-Chancellors Research and Teaching Fel-
lowship (Australia), Austrian Science Fund, Austrian Min-
istry of Science Research and Economy, FFG-ALR (con-
tract no. 844360), FWF (P24621-N27), Austrian Academy
of Sciences (Austria), MEC and MCTIC (Brazil), Generali-
tat de Catalunya (SGR 874, 2014-SGR-1295, CERCA pro-
gramme) and Barcelona City Hall (Catalonia), PIA CON-
ICYT (Grant No. PFB0824) and FONDECYT (grants
No. 1140635, 1150101, 1160400, 3170596, 11150325, Mile-
nio Grant RC130001, Becas Chile) (Chile), National Fun-
damental Research Program (Grant No. 2013CB336800),
National Natural Science Foundation of China (91121022,
61401441, and 61401443), Chinese Academy of Science
(Strategic Priority Research Program (B) XDB04010200),
and the 1000 Youth Fellowship program, National Natu-
ral Science Foundation of China (Grant 11674193), Sci-
ence and Technology Commission of Shanghai Municipal-
ity (grant 16JC1400402) (China), ERC (grant agreements
AQUMET 280169, 3DQUEST 307783, OSYRIS 339106,
ERIDIAN 713682, QITBOX, QUOLAPS, QuLIMA, Su-
perQuNet), ESA (contract no. 4000112591/14/NL/US),
FEDER, H2020 (QUIC 641122) and Marie Sk lodowska-Curie
programme (grant agreement 748549) (European Comission),
German Federal Ministry of Education and Research (projects
QuOReP and Q.com-Q) (Germany), CONACyT graduate
fellowship programme (Mexico), MINECO (FIS2014-60843-
P, FIS2014-62181-EXP, SEV-2015-0522, FIS2015-68039-P,
FIS2015-69535-R, FIS2016-79508-P, Ramon y Cajal fellow-
ship programme, TEC2016-75080-R), ICFOnest+ international
postdoctoral fellowship program (Spain), Knut and Alice Wal-
lenberg Foundation (project “Photonic Quantum Information”
) (Sweden), NIST (USA), AXA Chair in Quantum Informa-
tion Science, FQXi Fund, Fundaci´o Privada CELLEX, Fundaci´o
Privada MIR-PUIG, the CELLEX-ICFO-MPQ programme, Fun-
daci´o Catalunya-La Pedrera, and International PhD-fellowship
program “la Caixa”-Severo Ochoa.
Author contributions: CA instigator, MWM project lead.
Coordination, gamification and networking (ICFO): SC gen-
eral supervision, MM-P project management, MG-M, FAB, CA
gamification design and execution, JT prediction engine, AH,
MG-M, FAB Bellster recruitment and engagement strategy,
5
design and execution, CA web infrastructure and networking,
MWM, CA, JT main manuscript with input from all authors.
Experiments: 1
: GJP, RBP, FGJ, MMW, SS experiment de-
sign and execution. 2
: AGW, MR experiment design and
execution. 3
: J-WP supervision, J-WP, QZ, XM, XY, exper-
iment conception and design, ZW, LY, HL, WZ SNSPD fab-
rication and characterization, JZ SNSPD maintenance, M-HL,
CW, YL photon source design and characterization, J-YG, YL
software design and deployment, XY protocol analysis, XY, YL
data analysis, J-WP, QZ, CW, XY, YL manuscript, with input
from all. 4
: TS, AZ, RU supervision, conception and coor-
dination, BL, JH, DR experiment execution and analysis. 5
:
FS, MB, FA, GC, LS experiment execution and analysis, RC
theory support. 6
: HW, WR, KR, RG, DB experiment design
and execution. 7
: AW, JH, PK, YS, CKA, SK, TW, PM, AB,
MO, SG, CE experiment design and execution. 8
: ST, TL,
FK, GS, PV, OA, experiment design and execution. 9
: HdR,
PF, GH experiment design and execution. 10
: HdR, AS, AL,
MM, DR, OJ, AM experiment design and execution, DC, AA
theory support. 11
: MAL coordination, server communication,
LTK, IHLG, AGM experiment design and execution, CTS, AB
input data formatting, LTK, IHLG, AGM, CTS, AB, MAL data
analysis. 12
: GX coordination, FT optical setup, PG, AA, JF,
A. Cuevas, GC optical setup support, JC electronics design and
implementation, JC, FT, experiment execution, DM software,
GL, PM, FS experimental support, A. Cabello theory support,
JC, ESG, J-˚
AL data analysis. 13
: LKS, SN, MS, OM-L, TG,
SG, PB, EK, RM experiment design, execution and analysis.
Competing interests statement: The authors declare no com-
peting financial interests.
Correspondence and material requests should be addressed
to morgan.mitchell@icfo.eu.
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trarily small amount of measurement independence is sufficient
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6
Methods
I. “FREEDOM” IN BELL TESTS
The use of the term “free” to describe the choices in a Bell
test derives more from mathematical usage than from its usage
in philosophy, although the two are clearly related. Bell12 (see
Section II below) states that his use of “free will,” reflects the
notion of “free variables,” i.e., externally-given parameters, in
physical theories, as opposed to dynamical variables that are
determined by the mathematical equations of the theory.
If x,yare the settings in a Bell test, a,bare the outcomes,
and λis the hidden variable, any local realistic hidden variable
model is described by the conditional probability distribution:
P(a,b|x,y) = X
λ
P(a|x,λ)P(b|y,λ)P(λ). (1)
where P(·|·) indicates a conditional probability. Note that x
and yappear as free parameters, while aand bare contingent
variables whose statistics are given by the theory, i.e., by P(λ),
P(a|x,λ) and P(b|y,λ). The mathematical requirements for
this “freedom” are made evident by a more general description
in which the local realistic model includes also x,y, in which
case it specifies the joint probability
P(a,b,x,y) = X
λ
P(a|x,λ)P(b|y,λ)P(x,y|λ)P(λ). (2)
Using the Kolmogorov definition of conditional probability
P(A,B) = P(A|B)P(B), we find that Eq. (2) reduces to
Eq. (1), provided that P(x,y|λ) = P(x,y), i.e., provided that
the settings are statistically independent of the hidden vari-
ables. By Bayes’ theorem, this same condition can be written
P(λ|x,y) = P(λ) and P(x,y,λ) = P(x,y)P(λ). We note
that this does not require that xbe independent of y, nor
does it require that P(x,y) be unbiased. Similar observations
emerge from the more involved calculations required to assign
p-values to observed data in Bell tests3.
The above clarifies the sense in which the basis choices
should be “free.” The desideratum is independence from the
hidden variables that describe the particle behaviours, keep-
ing in mind that the particles could in principle be influenced
by anything within the backward light-cone of their measure-
ment. Because the setting choices and the measurements will
always have overlapping backward light-cones, it is impossible
to rule out all such influences based on space-time considera-
tions. It should also be noted that complete independence is
not required, although the tolerance for interdependence can
be low29.
A very similar concept of “freedom” applies to the entangled
systems measured in a Bell test. A Bell inequality violation
with free choice and under strict locality conditions implies in-
determinacy of the measurement outcomes, or else faster-than-
light communications and thus closed time-like curves10,21. If
Bob’s measurement outcome is predictable based on informa-
tion available to him before the measurement, and if it also
satisfies the condition for a Bell inequality violation, namely
a strong correlation with Alice’s measurement outcome that
depends on his measurement choice, then Bob can influence
the statistics of Alice’s measurement outcome, and in this way
communicate to her despite being space-like separated from
her. Considering, again, that Bob could in principle have infor-
mation on any events in his backward light cone, this implies
(assuming no closed time-like curves) that Bob’s measurement
outcome must be statistically independent of all prior events.
In this way, we see that “freedom,” understood as behaviour
statistically independent of prior conditions, appears twice in
a Bell test, first as a requirement on the setting choices, and
second as a conclusion about the nature of measurement out-
comes on entangled systems. These two are linked, in that the
second can be demonstrated if the first is present.
Prior tests using physical randomness generators to choose
measurement settings thus demonstrate a relationship between
physical processes, showing for example4,8 that if spontaneous
emission is “free,” then the outcomes of measurements on en-
tangled electrons are also “free.” By using humans to make
the choices, we translate this to the human realm, showing, in
the words of Conway and Kochen30, “if indeed there exist any
experimenters with a modicum of free will, then elementary
particles must have their own share of this valuable commod-
ity.” Here “experimenters” should be understood to refer to
those who choose the settings, i.e., the Bellsters.
II. JOHN STEWART BELL ON “FREE VARIABLES”
A brief but informative source for Bell’s positions on setting
choices is an exchange of opinions with Clauser, Horne and Shi-
mony (CHS)32, in articles titled “The theory of local beables”
and “Free variables and local causality.” In the first of these
articles Bell very briefly considers using humans to choose the
measurement settings
It has been assumed [in deriving Bell’s theorem]
that the settings of instruments are in some sense
free variables - say at the whim of experimenters -
or in any case not determined in the overlap of the
backward light cones.
while the second article defends this choice of method and
compares it against “mechanical,” i.e. physical, methods of
choosing the settings.
Suppose that the instruments are set at the whim,
not of experimental physicists, but of mechanical
random number generators. Indeed it seems less
impractical to envisage experiments of this kind...
Bell proceeds to consider the strengths and weaknesses of phys-
ical random number generators in Bell tests, offering arguments
why under “reasonable” assumptions physical random number
generators might be trusted, but nonetheless concluding
Of course it might be that these reasonable ideas
about physical randomizers are just wrong - for
the purpose at hand. A theory might appear in
which such conspiracies inevitably occur, and these
conspiracies may then seem more digestable than
the non-localities of other theories.
In sum, Bell distinguishes different levels of persuasiveness,
noting that physical setting generators, while having the re-
quired independence in many local realistic theories, cannot
7
be expected to do so in all such theories. In contemporary
terminology, what he argues here is that physical setting gen-
erators can only “tighten,” not “close” the “freedom-of-choice
loophole.”
Bell also defends his use of the concept of “free will” in a
physics context, something that had been criticized by CHS.
Bell writes
Here I would entertain the hypothesis that exper-
imenters have free will ... it seems to me that in
this matter I am just pursuing my profession of
theoretical physics.
. . . A respectable class of theories, including con-
temporary quantum theory as it is practiced, have
‘free’ ‘external’ variables in addition to those inter-
nal to and conditioned by the theory. These vari-
ables provide a point of leverage for free willed
experimenters, if reference to such hypothetical
metaphysical entities is permitted. I am inclined
to pay particular attention to theories of this kind,
which seem to me most simply related to our ev-
eryday way of looking at the world.
Of course there is an infamous ambiguity here,
about just what and where the free elements
are. The fields of Stern-Gerlach magnets could
be treated as external. Or such fields and mag-
nets could be included in the quantum mechanical
system, with external agents acting only on the ex-
ternal knobs and switches. Or the external agents
could be located in the brain of the experimenter.
In the latter case the setting of the experiment is
not itself a free variable. It is only more or less
correlated with one, depending on how accurately
the experimenter effects his intention.
It is clear from the last three sentences that Bell considers
human intention, i.e., human free will, to be a “free variable” in
the sense he is discussing. That is, he believes human intention
fulfils the assumptions of Bell’s theorem, as do experimental
settings faithfully derived from human intention.
III. USE OF “FREEDOM-OF-CHOICE LOOPHOLE” AND
“LOCALITY LOOPHOLE” IN THIS WORK
As noted above, a statistical condition used to derive Bell’s
theorem is P(x,y,λ) = P(x,y)P(λ), where xand yare
choices and λdescribes the hidden variables. This statistical
condition, known as the “freedom of choice assumption,” does
not distinguish between three possible scenarios of influence:
the condition could fail if the choices influence the hidden vari-
ables, if the hidden variables influence the choices, or if a third
factor influences both choices and hidden variables2,3,17.
By long tradition, the “locality loophole” (LL) is the name
given to the possibility of influence from Alice’s (Bob’s) choices
or measurements to Bob’s (Alice’s) measurement outcomes.
The term “freedom-of-choice loophole” (FoCL) was introduced
in Scheidl et al.17, to describe influence from hidden variables
to choices. The text of the definition is “the possibility that
the settings are not chosen independently from the properties
of the particle pair.” It is worth noting that this formulation
centres on the act of choosing and its independence, which
(assuming relativistic causality, an element of local realism)
can only be spoiled by influences from past events, not future
events.
Our use in this article follows the Schiedl et al. definition as
just described: FoCL refers to the possibility of influences on
the choices from any combination of hidden variables and/or
other factors within the backward light-cone of the choice,
while the possibility of influences from choices to hidden vari-
ables, which necessarily occur in the forward light-cone of the
choice, is included in LL. Such a division, in addition to fit-
ting the commonsense notion of free choice, avoids counting a
single possible channel of influence in both FoCL and LL.
IV. STATUS OF THE FREEDOM-OF-CHOICE LOOPHOLE
The FoCL remains unclosed after recent experiments si-
multaneous closing locality, detection efficiency, memory, tim-
ing, and other loopholes4–7 . Space-time considerations can
eliminate the possibility of such influence from the particles
to the choices5,6,17,34, or from other space-time regions to
the choices4,7, but not the possibility of a sufficiently early
prior influence on both choices and particles. To motivate
freedom of choice in this scenario, well-characterized physical
randomizers8,9 have been used to choose settings.
In experiments4–6 the physical assumption is that at least
one of: spontaneous emission, thermal fluctuations, or classical
chaos8is uninfluenced by prior events, and thus unpredictable
even within local realistic theories. In experiments7,17,34,37 the
physical assumption is that photodetection is similarly uninflu-
enced. While still requiring a physical assumption and thus not
“closing” the freedom-of-choice loophole, this strategy “tight-
ens” the loophole in various ways: First, by using space-like
separation to rule out influence from certain events, e.g. en-
tangled pair creation, and from defined space-time regions.
Second, by using well-characterized randomness sources, for
which the setting choice is known to faithfully derive from a
given physical process, it avoids assumptions about the pre-
dictability of side-channel processes. Third, in the case of4–6,8 ,
by using a physical variable that can be randomized by each of
several processes, the required assumption is reduced from “x
is uninfluenced” to “at least one of x, y and z is uninfluenced.”
FIG. 3. Web architecture of The BIG Bell Test.
8
0 1
p(0|0)
p(1|0)
p(0|1) p(1|1)
FIG. 4. Markov chain for L= 1.
V. PREDICTION ENGINE
Generation of random sequences by humans has been a sub-
ject of study in the field of psychology for decades39. Early
studies showed that humans perform poorly when asked to
produce a random sequence, choosing in a biased manner and
deviating from a uniform distribution. However, in40, it was
shown that humans can be trained to behave randomly by
playing a competitive zero-sum game in which uniform ran-
dom choices are the best strategy. One such game is matching
pennies: Players have to simultaneously choose between heads
or tails; one player wins if the results are equal, the other wins
if the results are different. This is a standard two-person game
used in game theory41 (see also42) with a mixed-strategy Nash
equilibrium: As both players try to outguess the other, by be-
having randomly they do not incentive either player to change
their strategy.
The BIG Bell Quest reproduces the coin-matching game,
with a machine-learning algorithm (MLA) playing the part of
the opponent. The MLA operates on simple principles that
human players could employ: it maintains a model of the ten-
dencies of the opponent, noting for example “after choosing
‘0,’ ‘0,’ she usually choses ‘1’ as her next bit.” The MLA
strategy operates with very little memory, mirroring the lim-
ited short-term memory of humans.
Formally, we will denote by {x1, ... , xn}a sequence of n
bits xi∈ {0, 1}. The goal of the prediction engine is, given
{x1, ... , xk}, with k<n, to produce a guess ˜xk+1 that matches
xk+1. After each prediction, the algorithm learns the actual
value xk+1 that the user has input and makes a new prediction
˜xk+2 for the next value of the sequence.
The prediction engine of the game should fulfill three basic
requirements: (i) it should perform well on human input of
relatively short sequences, (ii) it has to be simple enough to
be deployed in all the devices running the BIG Bell Test with-
out affecting the performance of the game (iii) it has to be
non-deterministic, in order to prevent users from learning and
exploiting the behavior of the algorithm.
To take into consideration short-term memory effects,
we shall model the user’s input as a discrete-time Markov
process43. The number of states will be determined by the
last Lbits of the sequence, giving rise to a 2L×2Ltransition
matrix
TL=p(~
x(L)
k+1|~
x(L)
k−L)~
x(L)
k+1,~
x(L)
k−L
where ~
x(L)
k=xk, ... , xk+L. Note that the columns of TLsum
to unity.
The transition probabilities p(~
x(L)
k+1|~
x(L)
k−L) are estimated from
the current sequence {x1, ... , xk}. Different values of Lgive rise
to different Markov chains (see Figs. 4 and 5).
For a fixed L, if the tail of the current sequence is ~
x(L)
k−L, we
p(00|00) p(01|01)
00 01
1110
p(00|01)
p(01|00)
p(10|11)
p(11|10)
p(11|00)
p(00|11)
p(10|01)
p(01|10) p(11|01)
p(01|11)
p(10|00)
p(00|10)
p(10|10) p(11|11)
FIG. 5. Markov chain for L= 2.
predict the next Lbits ˜x(L)
k+1 by looking at the most probable
outcome
˜x(L)
k+1 = arg max
~
x(L)
k+1
p(~
x(L)
k+1|~
x(L)
k−L). (3)
The length of the sequences that the players generate allow for
a reliable estimation of the transition probabilities for L<4.
Note, however, that the predictor is required to output only
the (k+ 1)-th bit of the sequence. Therefore, we can consider
the most probable jump for different values of L. The prediction
engine outputs then the first bit of ˜x(L0)
k+1 where L0is given by
L0= arg max
Lp(˜x(L)
k+1|~
x(L)
k−L). (4)
At this point, the prediction engine is deterministic. This im-
plies that there exists a sequence of bits such that the predictor
will always give a wrong result. To find it, one simply simu-
lates the predictor and flips the value of ˜xk+1. To defeat this
strategy, we initialize the matrix TL, by predicting a random
prefix of 10 bits.
VI. NETWORKING STRATEGY AND ARCHITECTURE
The BBT required reliable, robust, and scalable operation
of two linked networking tasks: providing the BIG Bell Quest
video game experience, and live aggregation and streaming of
user input to the running experiments. From a networking per-
spective, the latter task resembles an instant messaging service,
with the important asymmetry that messages from a large pool
of senders (the Bellsters) are directed to a much smaller pool
of recipients (the labs). The network architecture is shown in
Fig. (3), and was implemented using Amazon Web Services
IaaS (Infrastructure as a Service) products.
In the messaging component, we employed a two-layered ar-
chitecture, shown in Fig. (3). In the first layer Big Bell Test
nodes received input bits from the users and performed a real-
time health check, described below, to block spamming by
robot “participants.” The data were then sent to the second
layer, a single instance Hub node that concatenated all the
9
bits from the first stage and distributed them to the labs. The
communication between the two layers was implemented us-
ing a memcache computation node to maximise speed and to
simplify the synchronisation between the two layers.
The gaming task was handled by a single layer of Game
nodes and a database. To protect the critical messaging task
from possible attacks on the gaming components, we used sep-
arate instances to handle backend gaming tasks, such as user
information and rankings, and to handle backend tasks in the
messaging chain, such as data logging. Load balancers, net-
working devices that distribute incoming traffic to a scalable
pool of servers, were used in both the gaming and messaging
front ends to avoid overloading. This design pattern is known
as horizontal scaling, and is a common practice in scalable
cloud systems.
We now give more details on each computational resource.
A. Big Bell Test nodes
The first layer of computing resources received data from
Bellsters, or more precisely from the BIG Bell Quest running in
browsers on their computers and devices. A variable number of
servers running the same software functionalities were placed
behind a pre-warmed load balancer that was prepared to sup-
port up to 10,000 simultaneous connections. Users connected
to the load balancer via a public URL end-point, and sent the
data from their browsers using websocket connections. This
first layer of servers aggregated the data from each connection
(i.e. from each user) in independent buffers during a T= 0.5 s
interval.
A simple but important “health check” was performed to
identify and block high-speed robotic participants. If a given
user contributed more than ten bits in a single interval, cor-
responding to a rate of at least 22 keypresses per second, the
user account was flagged as being non-human and all subse-
quent input from that user was removed from the data stream.
No feedback was provided to the users in the event their ac-
count was flagged, to avoid leaking information on the blocking
mechanism. This method could potentially ban honest users
due to networking delays and other timing anomalies, but was
necessary to prevent the greater risk that the data stream was
flooded with robotic input.
B. Hub node
The Hub node aggregated the data from all the Big Bell Test
nodes and also handled the connection to the labs. In contrast
to the Big Bell Test nodes, which had to service connections
from an unknown and rapidly changing number of users, the
Hub node was aggregating data from a small and relatively sta-
ble number of trusted instances. Overall, the two layer design
simplified the networking task of delivering input from a large
and variable number of users to end points (the labs) receiving
aggregated data streams at variable rates.
Laboratories connected to the Hub instance to receive ran-
dom bits from the Bellsters. As with the Big Bell Test in-
stances, these connection were established using websocket
connections. When connecting to the Hub node, the labs
specified their bitrate requirement, which could be dynami-
FIG. 6. Screenshot of in-game feedback given to Bellsters,
showing use of their input bits in running experiments. Blue and
Red buttons allow instant sharing on social networks Twitter
and Weibo, respectively.
cally changed. The Hub node then sent a stream of Bellster-
generated bits at the requested rate. In the event that insuffi-
cient Bellster-generated bits were arriving in real-time, archived
bits from BBT participation prior to the day of the experiment
were distributed to the labs in advance.
C. Memcache node
The interface between The Big Bell Test nodes and the Hub
instance was implemented using a memcache node. While
adding an extra computing resource slightly increased the com-
plexity of the architecture, it added robustness and simplified
operations. The memcache node, in contrast to the Big Bell
Test and Hub nodes, had no internet-facing functionality, mak-
ing its operation less dependent on external conditions. For this
reason, both the Big Bell Test nodes and the Hub node were
registered and maintained on the memcache node, allowing the
restart of any of these internet-facing instances without loss of
records or synchronisation.
In addition, and as detailed in the next section, there was an
additional Monitor node in charge of (i) recording all the ran-
dom bits that were being sent from the Bellsters to the labs,
and (ii) providing real-time feedback to the Bellsters. This
functionality was isolated from the operations of the Hub node.
Again, by splitting the Monitor and Hub instances, a failure or
attack in the public and non-critical real-time feedback func-
tionality had no effect on the main, private, and critical random
bit distribution task.
D. Monitor node
For analysis and auditing purposes, all of the bits passing
through the first layer of servers were recorded in a database,
together with metadata describing their origin (Monitor com-
puting resource in Fig. (3)). In particular, every bit was stored
10
together with the username that created it and the origin times-
tamp. The random bitstreams sent to the individual labs were
similarly recorded bit-by-bit, allowing a full reconstruction of
the input to the experiments.
In post-event studies of the input data, we estimated the pos-
sible contribution from potentially machine-generated partici-
pations that were not blocked by the real-time blocking mecha-
nism. We analysed participants whose contribution were signif-
icant, more than 2 kbit bits in total, and looked for anomalous
timing behaviours such as improbably short time spent between
missions and improbably large number of bits introduced per
mission, both of which are limited by the dynamics of human
reactions when playing the game. Flagging participants that
contributed such anomalous participations as suspicious, and
cross-referencing against the bits sent to the experiments, we
find that no experiment received more than 0.1% bits from
suspicious participants.
In the Monitor computing resource, in addition to being used
to store in a database all the information that was streamed
to the labs, we also implemented a real-time feedback mecha-
nism to improve the Bellsters’ participation experience. After
accomplishing each mission, users were shown a report on the
use of their bits in each of the labs running at that moment, as
illustrated in Fig. 6. The numbers shown were calculated as a
binomial random process B(n,pi) with parameters n=Nand
pi=Ri/R, where Nis the number of bits introduced by a user
in his/her last mission, Riis the number of bits sent to lab i,
and Ris the total number of bits entered in the last T= 0.5 s
interval.
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31 G. P¨utz, D. Rosset, T. J. Barnea, Y.-C. Liang, N. Gisin, Arbi-
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to manifest quantum nonlocality, Phys. Rev. Lett. 113, 190402
(2014).
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ence & Business Media, 2009).
11
1
Quantum steering using human randomness
Authors: Raj B. Patel, Farzad Ghafari Jouneghani, Morgan M. Weston, Sergei Slussarenko, and Geoff J. Pryde
FIG. 7. Experimental setup. Alice and Bob’s measurements stages are set according to the random stream of bits acquired from
the Big Bell Test server. Entangled photon pairs are generated by pumping a sandwiched Type-I BiBO crystal with a continuous
wave laser diode at 404 nm. Each photon from the down-converted pair is sent along an optical fiber to polarisation analysis stages,
one for Alice and one for Bob. Photons are detected using silicon avalanche photodiode detectors and the electrical signals for each
event time-tagged. A computer is used to calculate the steering parameter S16 in real-time. As additional random measurement
settings are retrieved from the server, the experiment is iterated for improved statistics.
Schr¨odinger first coined the term ’steering’44 as a generalisation of the EPR-paradox. With the advent of quantum technolo-
gies, steering has been recognised as being well suited to certain quantum communication tasks. Here we report a demonstration
of EPR-steering using polarisation entangled photons, where Alice and Bob’s measurement settings are chosen based on data
randomly generated by humans. We use a 404 nm UV continuous wave laser diode to pump a pair of sandwiched type-I nonlinear
bismuth triborate (BiBO) crystals to generate entangled photon pairs at 808 nm via spontaneous parametric down-conversion.
The generated state is the singlet state |ψi=1
√2(|HAVBi − |VAHBi). The generated photon pairs are sent to two separate
measurement stages consisting of polarisation analysers and single-photon avalanche photodiode detectors. The stages, desig-
nated Alice and Bob, were located 50 cm apart from one another. Single photons are measured shot-by-shot. That is, for each
random measurement setting, a short burst of detection events are collected and time-tagged. From this set of detections, only
the very first joint detection is kept and the others are discarded.
During the Big Bell test event, bits were acquired at a rate of 4 bps for 24 hours. A random four bit sequence represents
one of n= 16 measurement settings per side. After performing all sixteen measurements, the following steering inequality was
calculated, S16 =1
n
n
P
k=1 AkσB
k≤Cn(refs45,46). Here S16 is referred to as the steering parameter whilst Ak∈ {−1, 1}and
σB
kis Alice’s measurement outcome and the Pauli operator corresponding to Bob’s measurement setting, respectively. The
correlation function is bounded by +1 (maximal correlations) and -1 (maximal anti-correlations) with a value of 0 representing
no correlation at all. It should be noted that fair sampling of all the detected photons is assumed. Given these parameters we
obtain S16 = 0.965 ±0.008 which beats the bound of C16 = 0.511 by 57 standard deviations. This is first demonstration of
12
quantum steering with human-derived randomness.
44 E. Schr¨odinger, Discussion of probability relations between separated systems, Mathematical Proceedings of the Cambridge Philosophical
Society 31, 555563 (1935).
45 D. J. Saunders, S. J. Jones, H. M. Wiseman, G. J. Pryde, Experimental EPR-steering using bell-local states, Nature Physics 6, 845
(2010).
46 A. J. Bennet, et al., Arbitrarily loss-tolerant Einstein-Podolsky-Rosen steering allowing a demonstration over 1 km of optical fiber with
no detection loophole, Phys. Rev. X 2, 031003 (2012).
13
2
Entanglement in Time
Authors: Martin Ringbauer, and Andrew White
FIG. 8. (a) The experimental setup used to test quantum entanglement in time. A single photon, produced by spontaneous
parametric down-conversion (not shown), is first measured by Alice, then by Bob and finally by Charlie. Alice and Charlie use a
half-wave plate (HWP) and a Glan-Taylor polarizer (GT) for their measurement, while Bob, being in the middle, measures the
quantum system indirectly by entangling it to another photon (using a partially polarizing beam splitter, PPBS) and detecting that
photon in an avalanche photo diode (APD). All three observers choose their measurement settings by using the human-generated
random bits supplied by the Bellsters to set the angles of their waveplates. (b) Measurement settings. Visualization of the
measurement settings for Alice (A0,A1), Bob (B0,B1), and Charlie (C0,C1) on the single-qubit Bloch-sphere. (c) Experimental
results. Shown is the cumulative violation of the CHSH inequality in time between the observers Alice and Bob (blue), and between
Bob and Charlie (orange) versus the number of observed detection events. The data shows a strong violation of both inequalities
and thus a violation of entanglement monogamy. The shaded regions correspond to 1σstatistical confidence intervals.
In the scenario originally considered by Bell47, pairs of entangled particles are shared between two observers, Alice and Bob,
who each perform one of two measurements on their particle of the shared pair at random. Since Alice and Bob are considered to
be spacelike separated, their particles cannot communicate during the measurements and thus all correlations observed between
Alice and Bob must have been present when the particles were created. Yet if their measurement statistics violate a Bell
inequality, they find that their particles are more strongly correlated than could be explained by pre-existing correlations—they
are entangled. Quantum entanglement, however, is not limited to the situations where the measurements are spacelike separated.
Alice and Bob could equally well be separated in time and perform their measurements on the same quantum system, one after
the other. Such an experiment can reveal entanglement in time or temporal entanglement, and just like in the spatial case, one
can derive a Bell-inequality to test for this kind of entanglement48.
Experimentally we test quantum entanglement in time using the setup in Fig. 8a, where a single photon is subject to a
sequence of three polarization measurements, first by Alice, then Bob, and finally Charlie. Each party uses the human-generated
random numbers supplied by the Bellsters to choose from two possible measurement settings, which correspond to two different
angles of the respective half-wave plates, see Fig. 8a-b. Since the measurements are timelike separated, there is no question
of locality and hence no need for fast switching or careful separation of measurement choices. It is, however, crucial that the
measurement choices are random and independent from each other, see Ref.49,50 for more details.
During the Big Bell Test our experiment used 6300 human-generated random bits supplied by the Bellsters to control the
waveplates for Alice, Bob, and Charlie. For each setting we recorded 0.1sof data, resulting in an average of 1.5 events per
measurement setting and outcome. Figure 8c shows the expectation values for the CHSH-Bell inequality in time between Alice
and Bob, and between Bob and Charlie as a function of the number of recorded events. For the full data set we obtain CHSH
values of Sab = 2.75 ±0.05 and Sbc = 2.79 ±0.05, corresponding to a violation of the classical bound of S= 2 by more than 15
standard deviations. This not only demonstrates entanglement in time, but also highlights a crucial difference between spatial
and temporal entanglement. A key property in the spatial case, known as monogamy of entanglement51 , is that entanglement
between Alice and Bob precludes either of them to be entangled with a third party. In contrast, our results show that in the
temporal case Bob can be entangled to Alice, and at the same time to Charlie, see Ref.49 for more details.
47 J. S. Bell, On the Einstein Podolsky Rosen Paradox, Physics 1, 195 (1964).
48 C. Brukner, S. Taylor, S. Cheung, V. Vedral, Quantum Entanglement in Time, arXiv preprint arXiv:quant-ph/0402127 (2004).
49 M. Ringbauer, et. al, Manuscript in preparation (2017).
50 M. Ringbauer, R. Chaves, Probing the non-classicality of temporal correlations, Manuscript in preparation (2017).
51 V. Coffman, J. Kundu, W. K. Wootters, Distributed entanglement, Phys. Rev. A 61, 052306 (2000).
14
3
Bell tests with imperfectly random human input
Authors: Yang Liu, Xiao Yuan, Cheng Wu, Weijun Zhang, Jian-Yu Guan, Jiaqiang Zhong, Hao Li, Ming-Han Li, Sheng-Cai Shi,
Lixing You, Zhen Wang, Xiongfeng Ma, Qiang Zhang and Jian-Wei Pan
FIG. 9. Bell test using imperfect input randomness. (a) A bird’s-eye view of the entanglement source, Alice’s detection and Bob’s
detection. The distances from the source to Alice and Bob are 87 ±2m and 88 ±2m, respectively. (b) Schematic setup of the
Bell test. A distributed feedback (DFB) laser diode (LD) at λ= 1560 nm is modulated to produce pulses with a repetition rate of
100 kHz and a pulse width of 10 ns. The pulses are amplified with an erbium-doped fiber amplifier (EDFA) and then are up-converted
to 780 nm via second-harmonic generation (SHG) in an in-line periodically poled lithium niobate (PPLN) waveguide. The residual
1560 nm light is filtered with a wavelength-division multiplexer (WDM) and a shortpass filter. After adjusting the polarization
using a half-wave plate (HWP) and a liquid crystal (LC), the 780 nm pump light is focused to a periodically poled potassium titanyl
phosphate (PPKTP) crystal in a “Sagnac” geometry to generate entangled photon pairs. A series of dichroic mirrors (DMs) are
used to remove the residual pump light at 780 nm and fluorescence before the entangled pairs are collected. In Alice’s and Bob’s
detection stations, a polarization controller (PC), a quarter-wave plate (QWP), a HWP and a polarizing beam splitter (PBS) are
used to set the measurement angle. Random numbers control the Pockels cells to dynamically select the bases. Superconducting
nanowire single-photon detectors (SNSPD) are used to detect the photons after the PBS.
Human randomness is very attractive for Bell tests, because of the element of human free will. Humans are not perfectly
random, however, and tend to produce patterns that make their choices somewhat predictable. For example, we ran the NIST
statistical test on the human-generated random numbers from the BBT and of the 14 different tests for uniformity, the human
random numbers only passed 2. If this predictability were related to the hidden variable λ, and if it were strong enough, it could
explain a Bell inequality violation within local realism.
The sensitivity of an experiment to setting/hidden-variable interdependence can be quantified: if a,band x,ydenote the
binary outputs and inputs, respectively, then the imperfection of the input randomness can be characterized by a bound on the
conditional setting probability P(xy|λ)
l= min
xyλP(xy|λ). (5)
where l∈[0, 1/4] and a smaller value of lindicates more imperfection of the input randomness. We report two Bell tests, one
using the well-known Clauser-Horne-Shimony-Holt (CHSH)52 inequality and the other using the measurement dependent local
15
(MDL)53 inequalities. The MDL is designed to be more robust against influence on the settings. We observe large violations of
the two Bell inequalities and give the lrequired of the input human randomness to rule out local realism.
Our experimental setup is shown in shown in Fig. 9(b). A 1560 nm seed laser with frequency f= 100 kHz, width ∆t= 10 ns
is amplified and up-converted to 780 nm via second-harmonic generation (SHG). Pumped with this laser, entangled pairs are
generated in the Sagnac based setup, and then collected into single mode fibers for detection. The measurement devices
in Alice’s and Bob’s detection station are around 90 meters from the source, as shown in Fig. 9(a). The spatial separation
makes sure the measurement in Alice’s detection station will not affect that in Bob’s detection station, and vice versa. A
field-programmable gate array (FPGA) board is used to generate synchronizing signals and to distribute the random numbers in
real time. ICFO provided us the human generated random numbers, which we re-distribute to modulate the basis immediately.
Note that the system only works when there is a batch of random numbers comes in. The random numbers control the Pockels
cell by applying a zero or a half-wave voltage, setting the basis to A0/A1for Alice and B0/B1for Bob. Passing through the
PBS, the photons are finally detected with a superconducting nanowire single-photon detectors (SNSPD), and recorded by a
time-digital convertor (TDC) for off-line data analysis.
First, the maximum entangled state |Ψ+i= (|HV i+|VHi)/√2 is generated and tested. We measure the visibility in
the horizontal/vertical basis as 99.2% and in the diagonal/anti-diagonal basis as 98%. State tomography shows the fidelity
to the ideal state is around 97.5%. We test the standard CHSH inequality with quantum random numbers, calculate the
value S= 2.804, with E(A1,B1) = −0.751, E(A1,B2) = 0.651, E(A2,B1) = 0.657, E(A2,B2) = 0.745 where E(Ax,By)≡
P(−1)a+b+xy p(ab|xy ). Considering MDL correlation with the randomness measure l, that is P(xy |λ)≥l,∀xy λ, the maximal
achievable CHSH value with MDL correlation is 4(1 −2l)53,54. To achieve the experimentally obtained Bell value with MDL
correlation, we thus need 4(1 −2l)<S= 2.804 and thus l<0.1495. In other words, if the input human randomness is high
enough, i.e., if l>0.1495, the experimentally observed data cannot be explained with any MDL correlation.
Next, the human random numbers are used to test the MDL inequality53 which is defined by lP(0000) −(1 −3l)[P(0101) +
P(1010) + P(0011)] ≤0. Interestingly, as long as P(xy|λ)≥l, such an inequality cannot be violated with any MDL correlation.
In this case, observing the violation of the MDL inequality indicates the existence of non-classical correlation even in the presence
of measurement dependence.
The non-maximal entangled state cos(69.1◦)|HV i+ sin(69.1◦)|VHiis generated. State tomography shows the fidelity to the
ideal state is 98.7%. Using the setup described above, the locality loophole is closed by considering the spatial distance and
the randomness loophole is closed with human free will. The experiment was performed during 30 Nov. and 1 Dec. when the
public helps us to generate random numbers. The coincidence values were tested with human-generated bits determining the
basis choices. The experimental data are divided into to several one-hour periods for statistical analysis.
As this MDL inequality cannot be violated with MDL correlation satisfying P(xy|λ)≥l,∀xyλ, we calculate the smallest
possible value of lsuch that the equal sign is saturated. In experiment, we obtain l= 0.10 ±0.05 for MDL inequality by using
human random numbers. As a comparison, we also use quantum random numbers to choose the basis. With the rest of the
setup remaining the same, we obtain l= 0.106 ±0.007 which gives a similar lvalue with less fluctuation. This is because the
total amount of data using quantum random numbers is much larger than using human random numbers. The input of human
random numbers was at most a few thousand per second whereas for quantum random numbers we had a steady 100 kbps for
controlling the basis. In total, we accepted and used around 80 Mb of human random numbers for the MDL inequality test in
two days. For comparison, we tested the inequality with quantum random numbers in around one and half hours, using more
than 500 Mbits.
52 J. F. Clauser, M. A. Horne, A. Shimony, R. A. Holt, Proposed experiment to test local hidden-variable theories, Phys. Rev. Lett. 23,
880 (1969).
53 G. P¨utz, D. Rosset, T. J. Barnea, Y.-C. Liang, N. Gisin, Arbitrarily small amount of measurement independence is sufficient to manifest
quantum nonlocality, Phys. Rev. Lett. 113, 190402 (2014).
54 X. Yuan, Q. Zhao, X. Ma, Clauser-horne bell test with imperfect random inputs, Phys. Rev. A 92, 022107 (2015).
16
4
Violation of a Bell Inequality using Entangled Photons and Human Random Numbers
Authors: Bo Liu, Johannes Handsteiner, Dominik Rauch, Rupert Ursin, Thomas Scheidl and Anton Zeilinger
FIG. 10. Experimental setup. The wavelength of the laser is 405nm. MBC: measurement basis controller; Pol Ctrl: polarization
controller; DM: dichroic mirror; HWP: half-wave plate; EOM: electro-optical modulator; PBS: polarized beam splitter; TTM: time
tagging module; PPS: pulse per second.
In the Big Bell test (BBT) experiment, we tested the CHSH form of the Bell inequality with polarization-entangled photon
pairs. As shown in Fig. 10, the entangled photon source was based on a Sagnac interferometer generating polarization-entangled
photon pairs in the maximally entangled state |Ψ−i=1
√2(|HAVBi−|VAHBi). Each photon pair was guided to two receivers,
called Alice and Bob, via single mode fibers. At each receiver, the entangled photons were coupled out of the fiber and guided
to an electro-optical modulator (EOM), which allowed for fast switching between complementary measurement bases. The
EOM was followed by a polarizing beam splitter (PBS) with a single-photon avalanche diode (SPAD) detector in each output
port. The EOM settings were driven by the measurement basis controller (MBC), which read the random bits from the BBT
server and converted them in real-time to the corresponding EOM control signals. In this way, real-time measurements in the
following linear polarization bases have been implemented for Alice (Bob): 0◦/90◦(22.5◦/112.5◦) if the random number was
’0’ and 45◦/135◦(67.5◦/157.5◦) if the random number was ’1’. Finally, using a time tagging module (TTM) and a computer,
Alice and Bob generated and recorded time stamps of all SPAD detection events, the EOM settings and an additional shared
pulse per second (PPS) signal.
FIG. 11. Coincidence counts between Alice and Bob for the experiment with human random numbers (HRN) mixed with quantum
random numbers (QRN).
On the BBT day, we performed measurements using all three different types of random numbers provided via the BBT
server, i.e. real-time human random numbers (HRN), quantum random numbers (QRN) and human random numbers from
the database (DB). In the first experiment, we used a mix of HRN and QRN for a total measurement time of 200 seconds.
During post-processing, we separated the results obtained with HRN from the results obtained with QRN. For the HRN (QNR)
data we obtained a Bell value of 2.6387 (2.6434) with a 81 (115) sigma violation of the local-realistic bound of 2. The second
17
experiment was performed with a mix of HRN and DB for a total measurment time of 210 seconds. For the HRN (DB) data we
obtained a Bell value of 2.6403 (2.6371) with a 63 (122) sigma violation of the local-realistic bound of 2. Errors are calculated
assuming Poissonian photon statistics. In our experiments, the time delay between Alice’s and Bob’s time-tags slightly varied for
the different detector combinations as can be seen from the coincidence peaks shown in Fig. 11. However, this could easily be
compensated during data post-processing, such that we could use a coincidence window of 1.25ns. All results are summarized
in detail in Table II.
TABLE II. Detailed measurement Results.
Exp # Time (s) Source RN rate (bps) Total CCs P1 P2 P3 P4 S Value Xigma Visibility
1 200 HRN 1612.88 160178 0.6520 -0.6947 -0.6592 -0.6329 2.6387 81.0265 0.9329
QRN 2727.68 294465 0.6560 -0.6938 -0.6544 -0.6391 2.6434 115.8174 0.9346
2 210 HRN 910.21 95024 0.6500 -0.7009 -0.6539 -0.6355 2.6403 63.0984 0.9335
DB 3404.49 337463 0.6498 -0.6984 -0.6589 -0.6300 2.6371 121.7927 0.9324
18
5
Experimental bilocality violation with human randomness
Authors: Luca Santodonato, Gonzalo Carvacho, Francesco Andreoli, Marco Bentivegna, Rafael Chaves and Fabio Sciarrino
FIG. 12. Experimental setup for bilocality test exploiting human randomness. Two couples of photons are independently
generated in the singlet state by a pulsed pump laser. For each pair, one photon is sent to one of the furthest stations (A or C,
respectively), while the other one reaches the central node B. All parties perform single qubit polarization analysis, exploiting Half
waveplates (HWPs) and Liquid Crystals (LC). The measurement choice is controlled by the random bits provided by the ICFO
BBT cloud infrastructure, which drives the voltage applied on the LC depending on the value of three random bits.
Nowadays, complex networks are attracting a large interest for the development of future quantum technologies but also
for the understanding of generalized Bell-like inequalities. By considering a tripartite scenario where two parties (Alice and
Charlie) share entangled states (independently generated) with a third one (Bob), we are able to witness a new kind of non-
classical behaviour called quantum non-bilocality55,56 where the results are incompatible with any possible model described
by two independent hidden variables. Alice, Bob and Charlie perform dichotomic measurements respectively labelled by the
variables x, y and z, and they return some binary outcomes described by the variables a, b and c. Since we are considering two
physically different and independent entangled sources we must consider also two different sets of hidden variables λ1and λ2.
Any correlation allowed by this model can be written as p(a,b,c|x,y,z) = Pλ1,λ2p(λ1)p(λ2)p(a|x,λ1)p(b|y,λ1,λ2)p(c|z,λ2).
The set of correlations compatible with the described model is constrained by the so-called bilocality inequality: B=p|I|+
p|J| ≤ 1 (with I=1
4Px,zhAxB0Czi,J=1
4Px,z(−1)x+zhAxB1Czi, (summing on x,z= 0, 1) and where: hAxByCzi=
X
a,b,c=0,1
(−1)a+b+cp(a,b,c|x,y,z)), which can be violated by quantum mechanics16?. In our experiment we implement a
photonic network consisting of three parties and two independent sources of quantum states (see Fig. 1) and we evaluate the
bilocality parameter B, exploiting random measurements settings driven by the bits provided by the Big Bell Test experiment.
This scheme allowed us to partially address the free-will loophole in this tripartite network context, providing the first proof-of-
principle experimental study of such loophole in Bell-tests involving more complex causal structures.
The choice of measurement settings in our stations was physically implemented by the use of liquid crystals, driven in real
time by the human random numbers provided by web users during the BBT day. This allowed us to witness a strong violation of
the bilocality inequality of B= 1.2251±0.0066 by cumulatively evaluation of the Bparameter for a growing number of collected
coincidences (see Fig. 2) observing a violation of almost 34 standard deviations. We kept each setting for 5 s, recorded the
coincidences in that time and then received fresh random bits for the next setting. Our experiment provides the first extension
to a quantum network with a more complex causal structure, and we were able to violate the bilocality inequality in real-time
(without post-processing of the data) by exploiting the human random bits. This experiment can pave the way towards more
complex studies involving networks and loophole free tests, and can have relevance as a cornerstone towards the implementation
of new quantum information protocols which exploit the resources of non-bilocal quantum correlations.
55 C. Branciard, N. Gisin, S. Pironio, Characterizing the nonlocal correlations created via entanglement swapping, Phys. Rev. Lett. 104,
170401 (2010).
56 C. Branciard, D. Rosset, N. Gisin, S. Pironio, Bilocal versus nonbilocal correlations in entanglement-swapping experiments, Phys. Rev.
A85, 032119 (2012).
19
0 10 000 20 000 30 000 40 000 50 000 60 000
0.8
0.9
1.0
1.1
1.2
1.3
1.4
Collected Fourfold
Coincidences
Bilocality Parameter
Classical Bilocal Correlations
Bilocal Bound
FIG. 13. Experimental bilocality violation with human randomness. We cumulatively evaluated the bilocality parameter
Band the total number of fourfold coincidences collected. A red line shows the bound of the bilocality inequality, which delimits
the classical bilocal region depicted with a shaded red area.
20
6
Violation of Bell’s inequality with a single atom and single photon entangled over a distance of 400 m
Authors: Kai Redeker, Robert Garthoff, Daniel Burchardt, Harald Weinfurter, Wenjamin Rosenfeld
atom trap
single-mode
fiber
fiber
BS
400 m
AOM
AOM
β
β'
select basis
α α'
CEM2e
CEM2i
700 m
read-out
MUX
PBS
APD
H+45
V-45
excitation
pulse
F=1
F'=0
52S1/2
52P3/2
(a) (b)
HWP
QRNG
BBT
Server
qrn
hrn2
hrn1
Lab 1 Lab 2
passive basis
choice
photon analysis
FIG. 14. (a) Scheme of the atomic levels involved in the entanglement between the spin state of the atom and polarization of the
photon. The atomic qubit consists of Zeeman spin states |mF=±1iof 52S1/2,F= 1 hyperfine ground level. (b) Overview of the
experiment. A single atom, trapped in Lab 2, is entangled with a single photon. The photon undergoes a polarization analysis in
Lab 1 where the measurement direction a∈ {α,α0}is passively selected at a beam-splitter (fiber BS). The measurement direction
on the atomic spin b∈ {β,β0}is actively selected using input from the BBT server and a local quantum random number generator
(QRNG).
We demonstrate a violation of a CHSH Bell inequality with a spin of a single trapped 87Rb atom which is entangled with
the polarization state of a single photon. The random numbers generated by human contributors were used here to decide
which measurement direction had to be applied to the atomic spin. Our experiment employs 3 different kinds of randomness:
randomness in detecting a photon in a certain output of an optical beam-splitter, a quantum random number generator and
human-generated random numbers.
In the experiment the generation of entanglement between the spin of the atom and polarization of the photon?is performed
by optical excitation as shown in Fig. 14(a). The subsequent spontaneous decay leads to the atom-photon state |ΨiAP =
1
√2(|↓iz|Li+|↑iz|Ri) where |↑izand |↓izare the atomic spin states and |Li,|Ridenote the left- and right-circular polarization
states of the photon (corresponding to |↓iz,|↑izstates of the photonic spin, respectively). The emitted photon is coupled into
a single-mode fiber and guided to another laboratory which is located at a distance of 400 m, Fig. 14(b). There the photon
passes a polarization-independent 50 : 50 beam-splitter (BS) where the (passive) choice is made which basis will be used for
the photon measurement according to probabilistic rules of quantum mechanics. In one output of the BS the measurement is
performed in the H/Vbasis by means of a polarizing beam-splitter (PBS) and two avalanche photo-diodes (APDs). In the
other output of the BS the measurement is performed in the ±45◦basis with the help of an additional half-wave retarder plate
(HWP) oriented at 22.5◦.
After the state of the photon was measured the read-out of the atomic state is performed. Here, for each measurement round,
two random numbers are retrieved from the server. The first one (hrn1) decides whether in the current round the measurement
direction shall be selected by a local quantum random number generator (QRNG)?or a human contributor. For these means
the QRNG output (qrn) and the second random number (hrn2) from the server are fed into a multiplexer (MUX). Its output
activates one of the two acousto-optical modulators (AOMs) thereby determining the polarization of an optical read-out pulse
applied to the atom. This polarization defines the basis for the analysis of the atomic spin (some details on the read-out
process can be found in?). The outcomes of the atom and photon measurements are combined into the CHSH Bell parameter
S=|hσασβi−hσασβ0i| +|hσα0σβ0i+hσα0σβ0i| in terms of correlators hσaσbi=1
Na,b(N↑↑
a,b+N↓↓
a,b−N↑↓
a,b−N↓↑
a,b), NA,B
a,bbeing
the number of events with the respective outcomes A,Bfor measurement directions a∈ {α,α0},b∈ {β,β0}.
During the experimental run of about 13 hours 39614 events were collected, 19716 where atomic measurement direction was
chosen by a human random number and 19898 events where this choice was done according to the local QRNG. The results
are S= 2.427 ±0.0223 for the first set and S= 2.413 ±0.0223 for the second, respectively. Both sets show a strong violation
of Bell’s inequality by more than 18 standard deviations. No statistically significant difference in the results for the two sets can
be observed.
57 V. Bouchiat, D. Vion, P. Joyez, D. Esteve, M. H. Devoret, Quantum coherence with a single Cooper pair, Phys. Scr. T76, 165 (1998).
58 J. Koch, et al., Charge-insensitive qubit design derived from the Cooper pair box, Phys. Rev. A 76, 042319 (2007).
59 A. A. Houck, et al., Controlling the spontaneous emission of a superconducting transmon qubit, Phys. Rev. Lett. 101, 080502 (2008).
21
1m
1m
photon
analysis
Fiber
Channel
400m
QRNG
atom
trap
Lab 1
Lab 2
FIG. 15. Top view of the main campus of LMU. The photon analysis arrangement is located in the of the faculty of physics (Lab 1)
while the atomic trap in the basement of the department of economics (Lab 2). Map data was provided by?.
60 F. Motzoi, J. M. Gambetta, P. Rebentrost, F. K. Wilhelm, Simple pulses for elimination of leakage in weakly nonlinear qubits, Phys.
Rev. Lett. 103, 110501 (2009).
61 J. M. Gambetta, F. Motzoi, S. T. Merkel, F. K. Wilhelm, Analytic control methods for high-fidelity unitary operations in a weakly
nonlinear oscillator, Phys. Rev. A 83, 012308 (2011).
62 F. W. Strauch, et al., Quantum logic gates for coupled superconducting phase qubits, Phys. Rev. Lett. 91, 167005 (2003).
63 M. A. Castellanos-Beltran, K. D. Irwin, G. C. Hilton, L. R. Vale, K. W. Lehnert, Amplification and squeezing of quantum noise with a
tunable Josephson metamaterial, Nat. Phys. 4, 929 (2008).
64 J. F. Clauser, M. A. Horne, A. Shimony, R. A. Holt, Proposed experiment to test local hidden-variable theories, Phys. Rev. Lett. 23,
880 (1969).
65 J.-A. Larsson, Loopholes in bell inequality tests of local realism, J. Phys. A: Math. Theor. 47, 424003 (2014).
66 V. Bentkus, On hoeffdings inequalities, Ann. Probab. 32, 1650 (2004).
67 D. Elkouss, S. Wehner, (Nearly) optimal P values for all Bell inequalities, npj Quantum Information 2, 16026 (2016).
22
7
Violation of a Bell inequality using superconducting qubits
Authors: Johannes Heinsoo, Philipp Kurpiers, Yves Salath´e, Christian Kraglund Andersen, Adrian Beckert, Sebastian Krinner,
Paul Magnard, Markus Oppliger, Theodore Walter, Simone Gasparinetti, Christopher Eichler, Andreas Wallraff
FIG. 16. (a) False coloured photograph of the superconducting chip used for the Bell test experiment. Each of the four qubits,
of which the two central ones were used, has its own flux line (FL) and readout resonator (RR). Neighbouring qubits are coupled
through the coupling resonators (CR) with flux controllable effective interaction strength. To perform single qubit gates microwave
pulses are applied via drive lines (DL). Probe tones at frequencies f1and f2are applied to the Purcell filter (PF) to measure the
qubit states. (b) Depending on the bit string (x,y) received from the BBT server we execute one of the four quantum gate sequences
labeled SZ ,SX ,TZ and TX . Single qubit gates Rφ
yrotate the state vector around the y-axes of the Bloch sphere by an angle φ. The
state preparation single qubit gates (blue) and the c-phase gate (connected black dots) remain unchanged, while the single qubit
gates (green) applied prior to the correlation sensitive readout (yellow) depend on the input bits from the server. (c) The cumulative
Svalue and (d) pvalue as a function of time covering the entire period of the BBT, including all data (blue) and considering only
data with successful calibration results (orange). The classical and the non-signalling thresholds are indicated as dashed horizontal
lines.
The Bell test in this work is performed using two superconducting qubits68–70, referred to as Alice and Bob, which are located
about 1 mm apart from each other as shown in Figure 16a. The qubit transitions frequencies are set to ωA/2π= 5.963 GHz
and ωB/2π= 5.464GHz, respectively. Single qubit gates are performed by applying 580 MHz wide DRAG pulses resonant with
the respective qubit transition frequencies71,72. The c-phase two qubit gate is realized by non-adiabatically tuning the state
|11iinto resonance with the |02istate for half the oscillation period73.
For each pair of bits received from the Big Bell test (BBT) server we perform one trial of the experiment by executing
one of the four quantum circuits shown in Figure 16b, each of which corresponds to a specific pulse sequence played from an
arbitrary waveform generator (AWG). Each of the four sequences comprises the deterministic generation of an entangled state
1
√2(|0+i−|1−i) followed by a set of single qubit gates, which rotates the different measurement axes into the computational
basis prior to readout. The readout of the qubit state is achieved by measuring the qubit state dependent transmission through
the Purcell filter (see Figure 16a) recorded and processed with an analog to digital converter (ADC) and field programmable
gate array (FPGA). A single shot fidelity of 96.6 % and 93.2 % for Alice and Bob respectively is achieved by employing a
near-quantum limited travelling wave amplifier74. Between two sequential runs of the experiment, a wait time of 50µs≈5T1
allows the qubits to decay back to their ground state. The successful initialization of the qubits using this passive method is
verified by reading out the qubit state prior to each experimental run. The datasets with failed state preparation were discarded.
About every 20 min both the qubit transition frequencies and two qubit gate parameters were recalibrated. Moreover, Bell state
tomography was used to benchmark each round of calibration.
During the 48 hours of continiusly running experiments, 16.34 million human generated random numbers were used to
23
perform 8.17 million individual Bell measurements of which 7.69 had succeful state initialization and calibration. By counting
the different measured two qubit states for different basis choices we directly evaluate the CHSH inequality75. The resulting
S-value is shown in Figure 16c and converges to a final value of 2.271(1) in case all data is included and to 2.307(1) if datasets
with failed calibration are ignored. The observed S value is mostly limited by qubit readout fidelity and qubit decay during the
300 ns long pulse sequence.
The confidence of which the experiment violates the CHSH inequality is quantified by estimating the p-values for the data
under the hypothesis of a local hidden variable (LHV) model65 . The estimation based on the Bentkus’ inequality66 is shown
to be tight and accounts for all possible memory effects and input bias67. Note that the latter is crucial for reasonable p-value
estimation as BBT participants tended to input (1, 0) and (0, 1) pairs twice more often than (1, 1). We observed an exponentially
decreasing p-value with increasing number of trials as shown in Figure 16d. The exponentially descreasing p-value is expected
as long as the performance of the experiment is not degraded over time, which is ensured by our automated recalibrations.
The final p-value of about ∼10−4000 indicates that with high confidence locality is violated either by the incompleteness of a
classical description of reality under the additional assumption of free will of the participants or by a locality loophole in our
specific experimental setup.
68 V. Bouchiat, D. Vion, P. Joyez, D. Esteve, M. H. Devoret, Quantum coherence with a single Cooper pair, Phys. Scr. T76, 165 (1998).
69 J. Koch, et al., Charge-insensitive qubit design derived from the Cooper pair box, Phys. Rev. A 76, 042319 (2007).
70 A. A. Houck, et al., Controlling the spontaneous emission of a superconducting transmon qubit, Phys. Rev. Lett. 101, 080502 (2008).
71 F. Motzoi, J. M. Gambetta, P. Rebentrost, F. K. Wilhelm, Simple pulses for elimination of leakage in weakly nonlinear qubits, Phys.
Rev. Lett. 103, 110501 (2009).
72 J. M. Gambetta, F. Motzoi, S. T. Merkel, F. K. Wilhelm, Analytic control methods for high-fidelity unitary operations in a weakly
nonlinear oscillator, Phys. Rev. A 83, 012308 (2011).
73 F. W. Strauch, et al., Quantum logic gates for coupled superconducting phase qubits, Phys. Rev. Lett. 91, 167005 (2003).
74 C. Macklin, et al., A near-quantum-limited josephson traveling-wave parametric amplifier, Science 350, 307 (2015).
75 J. F. Clauser, M. A. Horne, A. Shimony, R. A. Holt, Proposed experiment to test local hidden-variable theories, Phys. Rev. Lett. 23,
880 (1969).
24
8
Telecom-compliant source of polarisation entangled photons for the violation of Bell inequalities driven
by human-generated random numbers
Authors: Florian Kaiser, Tommaso Lunghi, Gr´egory Sauder, Panagiotis Vergyris, Olivier Alibart, and S´ebastien Tanzilli
FIG. 17. (a) Experimental setup. A 780 nm continuous-wave laser pumps a PPLN/W placed in a Sagnac interferometer. This
way, polarisation entangled photon pairs are generated in the state |ψi=|Hsi|Hii+|Vsi|Vii/√2. After being deterministically
separated using a C/L-band WDM, the photons are directed to Alice and Bob. Both rotate, accordingly to the HRN, the polarisation
state of their respective photon with an EOM. Finally, the polarisation state is analysed using a PBS, followed by two SPDs. (b)
User settings that are applied at Alice’s and Bob’s stations accordingly to the HRN inputs, provided by the Bellsters. (c) Schematic
sketch of the data acquisition strategy. (d) Development of the 5-minute averaged S-parameter as a function of time. The four
vertical arrows indicate the times at which unexpected incidents occurred to the experiment.
We violate the Bell inequalities by more than 143 standard deviations using polarisation entangled photon pairs76–79. The
related experimental setup is shown in FIG. 17(a). We developed a photon pair source which is entirely based on guided-wave
photonics in order to guarantee the highest possible stability80.
Diagonally polarised light, |Di, from a fibre-coupled continuous-wave 780 nm pump laser passes through a wavelength division
multiplexer (WDM), which is the fibre optics equivalent of a bulk dichroic mirror. The subsequent fibre polarising beam-splitter
(PBS) defines the input and output of a fibre Sagnac loop80,81. Inside the loop, vertically (horizontally) polarised pump light
propagates clockwise (anti-clockwise) in polarisation maintaining fibres (indicated by blue lines). By rotating the right-hand side
fibre by 90◦, the horizontally polarised pump light is effectively turned to be vertical. The pump light is injected in a periodically
poled lithium niobate waveguide (PPLN/W) in which vertically polarised pump photons are converted to vertically polarised
signal and idler photon pair contributions through type-0 spontaneous parametric downconversion, i.e. |Vi → |Vsi|Vii. Here,
the subscripts sand idenote signal and idler photons at wavelengths of λs= 1570 nm and λi= 1550 nm, respectively. The
photon pair contribution obtained in the clockwise sense is rotated in the polarisation maintaining fibre, and therefore becomes
|Hsi|Hii. Both contributions, i.e. |Vsi|Viiand |Hsi|Hii, are then coherently combined at the PBS and separated from the
pump light using the WDM. It is important to note that we choose the pump laser power to be low enough such that the
source generates only one photon pair contribution at a time, i.e. the probability for generating both contributions |Vsi|Viiand
|Hsi|Hiisimultaneously is negligible. Therefore, the following maximally polarisation entangled photon pair state is generated:
|ψi=|Hsi|Hii+|Vsi|Vii/√2. Signal and idler photons are deterministically separated using a standard telecom C/L-band
WDM, filtered down to ∼1 nm bandwidth and further directed to Alice’s and Bob’s stations, which are separated by 35 m of
optical fibre, corresponding to a physical separation of 5 m. For entanglement analysis, both users are equipped with fibre
electro-optic phase modulators (EOM), allowing them to rotate the polarisation state of their respective photon on demand.
FIG. 17(b) shows the operations that Alice and Bob apply depending on the human random numbers (HRN) that are generated
by the Bellsters and provided by the central server at the ICFO82. The settings we use correspond to the standard ones for
25
violating the Bell inequality using polarisation entangled photons76–79. Finally, each user analyses the polarisation state of their
photon using a PBS, followed by two Indium Gallium Arsenide avalanche single photon detectors (SPD). A coincidence electronic
circuit is used to account only for events in which both Alice and Bob receive a photon from the same pair.
A schematic of our data acquisition scheme is shown in FIG. 17(c). Every two seconds, a table of 2 ×1000 random bits (Alice
and Bob) is downloaded from the ICFO server, and the following sequence is repeated 1000 times:
1. A 4 µs time window is reserved in order to adjust Alice’s and Bob’s EOM settings accordingly to the HRNs. During this
time, no coincidences are recorded. The following information is written into the raw data output file: a time stamp at
the end of the 4 µs window, and Alice’s and Bob’s EOM settings.
2. Two-photon coincidences are recorded for 996 µs. Time stamps and information about the corresponding pairs of detectors
are stored in the raw data output file.
3. Thereafter, the experiment is halted for one second to give the computer time to analyse the data and store them on the
hard-disk drive.
We note that during the second step in the above-mentioned procedure it might occur that no or multiple coincidence events
are recorded. This is why we construct a new data file from the raw data file. Here, no-coincidence events are deleted, and for
very rarely occurring multi-coincidence cases only the event belonging to the first time stamp is kept. Single coincidence events
are not modified and stored as is.
From the new data file, the S-parameter is constructed in real-time following the standard approach76–79. In FIG. 17(d), we
show the 25-hour time line of the measured S-parameter with a 5-minute running average. Within the first four hours, we
observe a drop due to a strong temperature change in our laboratory which caused a slight misalignment of the PPLN/W. At
∼3:20 pm, the photon pair coupling from the PPLN/W to PMFs was re-optimised, and the resulting S-parameter increased.
At ∼3:00 am the experiment was halted for about 10 minutes due to an electric power failure. A second realignment procedure
was required at ∼7:00 am due to a fast temperature change in the laboratory induced by the building air conditioning. Finally,
the experiment was halted a second time at ∼10:30 am due to a SPD overheating problem.
Note that none of the above-mentioned issues is actually related to the optical design of our fully guided-wave photon pair
source, but exclusively due to infrastructural influences that could not be controlled. Nevertheless, the S-parameter is maintained
always above 2 which exceeds the classical-quantum boundary, therefore proving the quantumness of our results.
The S-parameter, averaged over the full experiment, which started on 30.11.2016 at 11:09 am and ended on 01.12.2016 at
12:10 pm is calculated to be Sfull = 2.431 with a standard error of σfull =±0.003, corresponding to a violation of the Bell
inequalities by more than 143 standard deviations. Throughout the course of the experiment, the Bellsters provided us with
2×19.5 ·106HRNs, with which we performed 2.9 ·106successful measurements (coincidences).
76 J. S. Bell, On the Einstein Podolsky Rosen paradox, Physics 1, 195 (1964).
77 J. F. Clauser, M. A. Horne, A. Shimony, R. A. Holt, Proposed experiment to test local hidden-variable theories, Phys. Rev. Lett. 23,
880 (1969).
78 G. Greenstein, A. Zajonc, The Quantum Challenge: Modern Research on the Foundations of Quantum Mechanics, Jones and Bartlett
series in physics and astronomy (Jones and Bartlett Publishers, 2006).
79 M. A. Nielsen, I. L. Chuang, Quantum Computation and Quantum Information: 10th Anniversary Edition (Cambridge University Press,
New York, NY, USA, 2011), 10th edn.
80 P. Vergyris, et al., Fully guided-wave photon pair source for quantum applications, e-print arXiv 1704.00639 (2017). To appear in
Quantum Sci. Technol.
81 H. C. Lim, A. Yoshizawa, H. Tsuchida, K. Kikuchi, Wavelength-multiplexed entanglement distribution, Optical Fiber Technology 16,
225 (2010).
82 ICFO-Website (2016). www.thebigbelltest.org.
26
9
Bell test using entanglement between a photon and a collective atomic excitation, driven by human
randomness
Authors: Pau Farrera, Georg Heinze, Hugues de Riedmatten
FIG. 18. Schematic drawing of the experiment. Entangled atom-photon time-bin qubits are generated in a cold 87Rb ensemble
(T≈100µK) and analyzed via two imbalanced Mach-Zehnder interferometers. Abbreviations: W write pulse; w write photon; R
read pulse; r read photon; PC polarization controller; Pz piezo-elecric fiber stretcher; D+(−)
w(r)single photon detector.
Our experiment within the Big Bell Test involves the generation and analysis of entanglement between a photon and a
collective atomic excitation in a cloud of laser-cooled 87Rubidium atoms83. Herefore, we generate photon-atom entangled
qubits, which are encoded in the time-bin degree of freedom, as proposed in84.
As shown in Fig. 18, we follow the DLCZ (Duan-Lukin-Cirac-Zoller) protocol85 sending a double-peaked write laser pulse
(W) to probabilistically generate a write photon (w) which is paired with an excitation in the atomic cloud. The write pulse
interacts with many atoms, leading to an excitation that is delocalized over all the atoms, i.e., a collective atomic spin excitation
(“spin-wave”). Since this process can happen in any of the two time-bins, the photon and the atomic excitation are entangled
in the time-bin degree of freedom. The entangled state can thus be written as |Ψw,ai=1
√2|EwEai+eiϕ|LwLai, where Ew(a)
denotes a write photon (atomic excitation) generated in the early time-bin, Lw(a)denotes a write photon (atomic excitation)
generated in the late time-bin, and the phase ϕcan be controlled by changing the phase between the early and late time-bins
of the write and read pulses. In order to temporally distinguish the atomic excitations created in the two different time-bins,
we apply an homogeneous magnetic field to induce collective de- and re-phasings of the stored spin-waves86. Subsequently, the
atomic qubit can be converted into a photonic time-bin qubit (r) using a resonant double-peaked read laser pulse (R). This
converts the photon-atom entangled state into a photon-photon entangled state, which is more suited for the entanglement
analysis. The analysis is done with two imbalanced Mach-Zehnder interferometers and single photon detectors, which allow us
to perform qubit projective measurements in any basis that lies on the equator of the Bloch sphere87. The bases in which the
write and read qubits are projected depend on the phase delays φwand φrbetween the two arms of each interferometer. The
quantum correlations of the two photons is then assessed by the CHSH Bell parameter88
S=|E(φw,φr) + E(φw,φ0
r) + E(φ0
w,φr)−E(φ0
w,φ0
r)|(6)
where E(φw,φr)=[p++(φw,φr)−p+−(φw,φr)−p−+(φw,φr) + p−−(φw,φr)] /p(φw,φr) are the correlation coefficients,
pij (φw,φr) are the probabilities to detect coincidences between the write and read photons at detectors Di
wand Dj
r, and
p(φw,φr) = Pi,j=+,−pij (φw,φr).
In order to change the phase of the interferometers to the desired values of φw,φ0
w,φr, and φ0
r, a short part of the fiber
of the 40 m long interferometer arms is rolled around a piezo-electric ceramic cylinder. Applying a voltage Uwor Urto the
corresponding piezo cylinder stretches the fiber and therefore changes the phase delay between the two arms of the write or
the read interferometer. The random numbers generated by the participants of the Big Bell Test were used to decide which
voltage is applied to each interferometer, hence controlling the measurement bases. Trapped atom clouds were created at a
rate of 59 Hz. For each cloud, we performed 608 entanglement trials. The bases were changed in between each cloud and not
between each single trial because of the limited bandwidth of the piezo fiber stretcher. However, the typical write-read photon
coincidence detection probability per trial p(φw,φr) was between 10−6and 10−5. We can therefore say that for each detected
coincidence event, the bases were chosen randomly.
During the time window of the Big Bell Test we used the live human random numbers to randomly choose between predefined
phases in the two analysing interferometers to take the data shown in Fig. 19(a). Here, p++ is plotted as a function of Ur∝φr
for two different values of Uw∝φw. The two fringes are shifted by 114(9) degrees exhibiting visibilities of V1= 0.72(0.08)
(blue dots) and V2= 0.63(0.10) (green circles). These visibilities are sufficient to prove entanglement between both time-bin
qubits, as follows from the Peres separability criterion (V>1/3) under the assumption of equally distributed noise for all
27
FIG. 19. (a) Photon coincidence detection probability between detectors D+
wand D+
ras a function of the voltage applied to the
piezo of the read photon interferometer. The two different curves correspond to two different voltages applied to the piezo of the
write photon interferometer: Uw= 0 V (blue dots) and Uw= 0.296 V (green circles). (b) Accumulated CHSH Bell parameter Sas
a function of data acquisition time for the measurement with stored human random numbers.
possible outcomes89. However, the values didn’t surpass the threshold of V>1/√2≈0.707 to guarantee Bell-type non-local
correlations. We obtained similar visibilities without the use of human random numbers, which confirmed that the measurements
were affected by experimental instabilities during the required relatively long integration times of several hours.
After improving the long-term stability of the experiment, we redid a Bell test at a later stage with human random numbers
received and stored during the day of the Big Bell Test. Here, the human random numbers were used to switch randomly
between the four settings required for the measurement of the CHSH inequality. The experimental results of that Bell Test are
shown in Fig. 19(b). The data acquisition lasted 3 hours and 26 minutes, during which we performed 364800000 experimental
trials. In this time we recorded 1100 photon coincidence events which led to a final CHSH Bell parameter of S= 2.29 ±0.10.
This measurement shows a violation of the Bell inequality |S| ≤ 2 by approximately three standard deviations.
83 D. N. Matsukevich, et al., Entanglement of a photon and a collective atomic excitation, Phys. Rev. Lett. 95, 040405 (2005).
84 P. Farrera, G. Heinze, H. de Riedmatten, in preparation (2017).
85 L. M. Duan, M. D. Lukin, J. I. Cirac, P. Zoller, Long-distance quantum communication with atomic ensembles and linear optics.,
Nature 414, 413 (2001).
86 B. Albrecht, P. Farrera, G. Heinze, M. Cristiani, H. de Riedmatten, Controlled rephasing of single collective spin excitations in a cold
atomic quantum memory, Phys. Rev. Lett. 115, 160501 (2015).
87 I. Marcikic, et al., Distribution of time-bin entangled qubits over 50 km of optical fiber, Phys. Rev. Lett. 93, 180502 (2004).
88 J. F. Clauser, M. A. Horne, A. Shimony, R. A. Holt, Proposed experiment to test local hidden-variable theories, Physical Review Letters
23, 880 (1969).
89 A. Peres, Separability criterion for density matrices, Phys. Rev. Lett. 77, 1413 (1996).
28
10
Violation of a Bell inequality using high-dimensional frequency-bin entangled photons
Authors: Andreas Lenhard, Alessandro Seri, Daniel Riel¨ander, Osvaldo Jimenez, Alejandro M´attar, Daniel Cavalcanti, Margherita
Mazzera, Antonio Ac´ın, and Hugues de Riedmatten
FIG. 20. a) Experimental setup. Photon pairs are generated via cavity enhanced SPDC in multiple frequency modes. The pairs
are split and the Idler photons sent to Alice and Signal photons to Bob. At both ends there are EOMs, controlled by a RF phase
shifter and an amplifier while the RF source is shared. Before detecting coincidences, single frequency bins are selected by cavity
filters. The basis settings are chosen by HRN and a computer generates analog voltages (DAC) controlling the RF phases and
powers accordingly. b) Spectrum of the photons, illustrating frequency-bins. c) Modulation spectrum of Signal EOM.
We report a Bell inequality violation with high-dimensional frequency-bin entangled photons. Due to energy conservation,
photon pairs generated by spontaneous parametric down-conversion (SPDC) are naturally correlated in frequency, such that the
sum of the signal and idler frequencies is always equal to the frequency of the pump beam. One can then define frequency-bins
in the spectrum and find correlations between different spectral bins of the two photons, leading to so-called frequency bin
entanglement90. In our experiment, we generate narrowband photon pairs in discrete frequency modes by SPDC in an optical
parametric oscillator (OPO) operated below threshold91. One photon is at visible wavelength (606 nm) while the other is at
the telecommunication wavelength (1436 nm). The photon spectrum consists of around 8 equally spaced modes, separated
by the free spectral range of the cavity (FSR=424 MHz, see Fig. 20b). The two photons are separated deterministically and
sent to Alice and Bob for analysis. The measurement process uses electro-optic phase modulators (EOMs) driven at a radio
frequency (RF) corresponding to the FSR of the OPO (see Fig. 20c) to mix neighboring modes and introduce a phase shift.
Each measurement setting for Alice and Bob corresponds to a given modulation depth (aand b, set by the RF power) and to a
given phase (αand β, set by the RF phase). We select single spectral modes of the signal and idler photons via filter cavities
and detect the photons with single photon counting modules (SPCM). The full setup is illustrated in Fig. 20.
We observe two-photon interference fringes depending on the phase difference between signal and idler EOMs. We develop
a theoretical model for our setup from which we estimate the optimal experimental configurations leading to a violation of the
CH-inequality92 SCH ≤2. During the BBT day we used the human random numbers (HRN) to choose in real time one out
of four settings for (aiαibj;i,j= 0,1) while the second phase setting (βk;k= 0..15) was chosen out of 16 possible phases.
This allowed us to record full interference fringes. We kept each setting for 10 s, recorded the coincidences in that time and
then received fresh HRN for the next setting. Our experiment reaches S= 2.25(8), corresponding to a violation of the Bell
inequality by three standard deviations. After the BBT, new measurements with stored HRN have been made, considering only
the four best settings leading to the maximal violation. In this way data can be collected much faster, resulting in a violation
of 8.5 standard deviations93.
90 L. Olislager, et al., Implementing two-photon interference in the frequency domain with electro-optic phase modulators, New Journal
of Physics 14, 043015 (2012).
91 D. Riel¨ander, A. Lenhard, M. Mazzera, H. de Riedmatten, Cavity enhanced telecom heralded single photons for spin-wave solid state
quantum memories, New Journal of Physics 18, 123013 (2016).
92 J. F. Clauser, M. A. Horne, Experimental consequences of objective local theories, Phys. Rev. D 10, 526 (1974).
93 D. Riel¨ander, et al., Frequency-bin entanglement of ultra-narrow band non-degenerate photon pairs, manuscript in preparation (2017).
29
11
Violation of the CHSH inequality using polarization-entangled photons
Authors: Laura T. Knoll, Ignacio H. L´opez Grande, Agustina G. Magnoni, Christian T. Schmiegelow, Ariel Bendersky, and
Miguel A. Larotonda
FIG. 21. Experimental setup. A 405 nm diode laser generates degenerate photon pairs by spontaneous parametric downconversion
at 810 nm. A series of birefringent crystals placed at the pump beam and at the downconverted paths compensate temporal and
spatial walk-off ensuring a high degree of indistinguishability; state tomography characterization of the produced state is shown in
the inset . Random bit strings are retrieved from the BBT server and fed to the stepper motor drivers that control the projective
measurements via rotations of the waveplates. The photo shows an actual motorized waveplate mount. Coincidences are registered
with an FPGA-based detector and read by the control computer.
We show the results of a two-channel experiment to test a Clauser-Horne-Shimony-Holt (CHSH)-like inequality, using polar-
ization entangled photons. Photon pairs are generated by spontaneous parametric downconversion in a BBO type-I nonlinear
crystal arrangement, pumped by a 405 nm cw laser diode polarized 45 degrees with respect to both crystals. Both photons are
generated at 810 nm94. A series of birefringence compensating crystals included in the photon pair source guarantee a high level
of entanglement: a tomographic reconstruction of the output state of the source is shown at the top left inset on Fig. 21)95.
Polarization projections are performed with motorized waveplates, which are fed with the random strings generated at the BBT
cloud infrastructure. Two pairs of single-photon counting devices detect the incoming photons and send the detections to an
FPGA based coincidence counter.
The experiment was fully controlled using a single PC. Each experimental run consisted in the following sequence: a pair of
random bits were gathered from the BBT server data and fed into the waveplate stepper motor drivers. Once the polarization
projections were set, an FPGA-based coincidence counter started a repetition of 20 measurements on the four coincidence
detections D1∧D3, D2∧D3, D1∧D4and D2∧D4. The full setup is shown in Fig. 21. The brightness of our source and
a detection window of 200 µs for each measurement gave a single-channel coincidence probability below 0.1. In particular,
the mean D1∧D3coincidence number per measurement was µ=0.091 for one particular waveplate setting. This results on a
total mean coincidence number per single experimental run (i.e. the expected value of detecting a coincidence on any channel)
of ν=0.227. Statistics of occurrence of either of the above situations follow a Poisson distribution. This condition minimizes
the occurrence of multiple coincidences. Repetitions of the measurement increased its chance of success: we used the first
single-channel coincidence from the list of 20 measurements as the result from each run, therefore increasing the ”bit usage
efficiency” of the experiment up to 97.5%. This rate also takes into account discarded runs with simultaneous coincidence
detections. The total duration for each run was close to 2 s, which accounted for the mechanical rotation of the waveplates
and the measuring time. Overall, almost 34 kbit were required from the BBT server at the Buenos Aires Node; some of them
were used for initial and mid-term alignment of the optical setup.
The complete experiment carried out during the BBT day built statistics from 10033 polarization settings measured, and
resulted in a measurement of the S-parameter value of S=2.55(7), which implies a violation of the CHSH-Bell inequality that
bounds local correlations by 7 standard deviations. Figure 22 shows the evolution of the S-value obtained throughout the day.
The red-shaded area represents the statistical uncertainty derived from the measured CHSH test.
30
FIG. 22. Evolution of the CHSH test statistic “S” throughout the BBT day. Approximately 2000 experimental runs are sufficient
to obtain a violation of the inequality with 95% confidence level
94 L. T. Knoll, C. T. Schmiegelow, M. A. Larotonda, Remote state preparation of a photonic quantum state via quantum teleportation,
Applied Physics B 115, 541 (2014).
95 P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, P. H. Eberhard, Ultrabright source of polarization-entangled photons, Physical
Review A 60, R773 (1999).
31
12
Post-selection loophole-free energy-time Bell test fed with human-generated inputs
Authors: Jaime Cari˜ne, Felipe Toledo, Pablo Gonz´alez, ´
Alvaro Alarc´on, Daniel Martinez, Jorge Fuenzalida, Jean Cort´es, ´
Alvaro
Cuevas, Gonzalo Carvacho, Aldo Delgado, Fabio Sciarrino, Paolo Mataloni, Jan-˚
Ake Larsson, Ad´an Cabello, Esteban S. G´omez,
Gustavo Lima and Guilherme B. Xavier
FIG. 23. Experimental setup. Dashed and red lines represent electrical connections and free-space beams, respectively. The propagation
distance between the source to Alice is 15 m and from the source to Bob is 45 m, determined mainly by the length of the piezoelectric
spooled fiber-optical stretchers (10 m long for Alice’s interferometer and 40 m for Bob’s). Please see text for further details.
Energy-time Bell tests based on the standard and widely employed Franson configuration96 are affected by the post-selection
loophole97. The only experimentally demonstrated solution to this problem is the so-called “hug” configuration98,99. Here we
perform a fully automated Bell test for the first time with such a configuration. Human random numbers (HRN) provided
from the Big Bell Test (BBT) server are used to choose the settings for each detected event. The experimental setup is shown
in Fig. 23, where the source generates energy-time entangled photon pairs through the process of spontaneous parametric
down-conversion. A periodically poled potassium titanyl phosphate (ppKTP) 20 mm long waveguide crystal emits degenerate
type-II (orthogonally polarized) photon pairs at 806 nm, when pumped with a single-mode longitudinal continuous wave laser at
403 nm. The single-photons are deterministically split with a polarizing beam splitter (PBS), with each photon being coupled
to a single-mode fiber and then guided to one of the two bidirectional 50:50 fiber couplers whose outputs are then cross-sent to
Alice and Bob. The main characteristic of the “hug” configuration is the presence of two crossed (or “hugging”) Mach-Zehnder
interferometers (MZI) serving as the communication channel between the source and the communicating parties. Alice and Bob
place single-photon detectors at the outputs of each interferometer. The single-photon detectors are free-running silicon-based
single-photon avalanche detectors, DA1and DA2for Alice and DB1and DB2for Bob. The interferometers are asymmetrical, as
in the standard Franson scheme, with each consisting of a short (S) and a long (L) arm.
Each interferometer needs to be actively stabilized against environmental phase drifts. In order to do so, a reference laser
beam (852 nm) is superposed to the path of the single-photons in the source, before coupling to the single-mode fibers. The
intensity of this reference signal is detected by p-i-n photodiodes after both interferometers (split from the single-photons with
dichroic mirrors) and are used to close individual electronic control loops based on field programmable gate array (FPGA)
electronics. Each control loop employs a piezoelectric fiber-optical stretcher, capable of dynamically changing the length of the
fiber100. With each interferometer independently stabilized, electro-optical phase modulators (PMs) are used to apply a relative
phase difference in a short time window (5 µs), compared to the control response time. With such a technique the control in
itself is not disturbed, and thus independent settings may be applied while the two interferometers remain stable100.
A motorized delay line is used to adjust the long-short path difference in both interferometers to be within the coherence
length of the photon pair. Once this is achieved the following state is generated without the need for temporal post-selection:
|Φi= 1/√2(|SSi+ei(φa+φb)|LLi), where φaand φbare phase shifts within the long arm of Alice and Bob’s respective MZIs.
We test the well-known Clauser-Horne-Shimony-Holt (CHSH) inequality S=E(φa,φb) + E(φ0
a,φb) + E(φa,φ0
b)−E(φ0
a,φ0
b)101,
where E(φa,φb) = P11(φa,φb) + P22 (φa,φb)−P12(φa,φb)−P21 (φa,φb), with Pij (φa,φb) corresponding to the probability of a
coincident detection at Alice and Bob’s detectors iand jrespectively, while the relative phases φaand φbare applied to Alice
and Bob’s interferometers. For the maximum violation of the Bell CHSH inequality the phase settings are φa=π/4, φb= 0,
32
φ0
a=−π/4 and φ0
b=π/2.
For each measurement round two bits are used from the BBT server to choose one out of the four possible setting combinations
(two settings for Alice and two for Bob). The detection electronics (also FPGA-based) register if a coincident detection occurred,
and record the values for the employed phases. This is done at a rate of 52 kbit/s while consuming approximately 27 million
bits from the BBT database. The average expected values for the entire run are shown in Fig. 24a), with the cumulative S
parameter in Fig. 24b), whose final value is 2.4331 ±0.0218, corresponding to a violation of 19.87 standard deviations for a
total of 20676 detection events.
FIG. 24. Experimental results. a) Correlation functions Eas a function of the different settings for the CHSH inequality. Dashed lines
correspond to the value of Efor a maximal violation of the CHSH inequality. b) Cumulative CHSH violation (S parameter) as a function
of the amount of consumed bits. Dashed red lines represent the local bound (2) and the quantum bound (2√2). Error bars in both
subfigures represent the standard deviation.
96 J. D. Franson, Bell inequality for position and time, Phys. Rev. Lett. 62, 2205 (1989).
97 S. Aerts, P. Kwiat, J.-A. Larsson, M. Z˙ukowski, Two-photon franson-type experiments and local realism, Phys. Rev. Lett. 83, 2872
(1999).
98 A. Cuevas, et al., Long-distance distribution of genuine energy-time entanglement, Nature Communications 4, 2871 EP (2013).
99 G. Carvacho, et al., Postselection-loophole-free Bell test over an installed optical fiber network, Phys. Rev. Lett. 115, 030503 (2015).
100 G. B. Xavier, J. P. von der Weid, Stable single-photon interference in a 1 km fiber-optic mach–zehnder interferometer with continuous
phase adjustment, Optics Letters 36, 1764 (2011).
101 J. F. Clauser, M. A. Horne, A. Shimony, R. A. Holt, Proposed experiment to test local hidden-variable theories, Phys. Rev. Lett. 23,
880 (1969).
33
13
Using human generated randomness to to violate a Bell inequality without detection or locality loopholes
Authors: Lynden Krister Shalm, Martin Stevens, Omar Maga˜na-Loaiza, Thomas Gerrits, Scott Glancy, Peter Bierhorst, Emanuel
Knill, Richard Mirin, Sae Woo Nam
FIG. 25. Experimental setup. (a) The locations of the Source (S), Alice (A), and Bob (B). Each trial, the source lab produces a
pair of photons in the non-maximally polarization-entangled state |ψi ≈ 0.982 |HHi+ 0.191 |VV i, where H(V) denotes horizontal
(vertical) polarization. One photon is sent to Alice’s lab while the other is sent to Bob’s lab to be measured. Alice’s computed optimal
polarization measurement angles, relative to a vertical polarizer, are {a=−3.7o,a0= 23.6o}while Bob’s are {b= 3.7o,b0=−23.6o}.
Each trial, Alice and Bob each use a bit from the Bellsters to choose which polarization measurement to make. Panel (b) shows
the Pockels cell that Alice uses, and panel (c) shows Bob’s Pockels cell. Alice and Bob are (187 ±1) m apart from one another. At
this distance, in any given trial when Bob has completed his measurement, information traveling at the speed of light from Alice’s
Pockels cell firing is still (88.25 ±1.1) m away from his measurement setup (represented by the light front). When Alice completes
her measurement, Bob’s light front from his Pockels cell firing is (127.2 ±1.1) m away from her measurement apparatus.
We report a violation of a Bell inequality free of fair-sampling and locality assumptions. We use polarization-entangled
photons generated by a nonlinear crystal pumped by a pulsed, picosecond laser. The laser repetition rate is 79.3 MHz, and each
pulse that enters the crystal has a probability of ≈0.002 of creating an entangled photon pair. The two entangled photons from
each pair are then separated, with each one being sent to one of two measurement stations (187 ±1) m apart, named Alice
and Bob. At Alice and Bob, a Pockels cell and polarizer combine to allow the rapid measurement of the polarization state of
the incoming photons. Alice’s and Bob’s decisions on how to set their Pockels cells are dictated by the bits supplied by the Big
Bell Test participants (Bellsters). The photons are then detected using fiber-coupled superconducting single-photon nanowire
detectors, each operating at over 90% efficiency102.
Our experimental setup, shown in Figure 25, is nearly identical to the experimental setup used in the fully loophole-free Bell
Test conducted in 2015103. The primary difference is that random numbers used to set Alice’s and Bob’s polarization settings
are provided by the Bellsters instead of random number generators. Like the 2015 experiment, we consider the measurement of
Alice’s or Bob’s photon detection to be complete when the amplified electrical signal from Alice’s or Bob’s detector reaches the
input of the time tagger that records the outcomes. The polarization measurement is carried out using a high-voltage Pockels
cell. When this device switches states, it is possible for an electro-magnetic pulse to be emitted. If these electro-magnetic
signals travel at the speed of light, then Bob completes his measurement (294.4 ±3.7) ns before any signal from Alice’s Pockels
cell could arrive at his station. Similarly, Alice completes her measurement (424.2±3.7) ns before a switching signal from Bob’s
Pockels cell could arrive at her location. Under these conditions the implementation of Alice’s setting and Bob’s measurement
outcome are space-like separated from one another and vice-versa, so it is impossible for one station’s setting to influence the
other station’s measurement.
Testing the hypothesis of local realism requires repeating the experiment many times, each of which is called a trial. We then
compare the trials’ statistics to those that local realistic theories predict. In our setup we perform 100,000 trials per second.
This is limited by the speed of our Pockels cells at Alice and Bob. Because the probability of generating a photon pair with
each pump pulse is small, Alice and Bob look for photons generated by 15 successive pulses during each trial. This increases our
probability of creating a photon pair per trial by more than an order of magnitude, allowing us to achieve a stronger violation
34
using fewer trials. Each trial then consists of 15 different time bins in which Alice and Bob may register photon detections. In
our experiment we collected data for just under 7 minutes and performed 40,559,990 trials. Each trial, Alice and Bob each used
one bit provided by the Bellsters to set their polarization measurement choice (consuming a total of 81,119,980 bits over the
course of the experiment). Immediately after collecting data using bits provided by the Bellsters, we repeated the experiment
using random bits provided solely by computer-based random number generators located at both Alice and Bob. In this second
data run we performed a total of 74,400,000 trials.
Each trial, Alice uses a bit from the Bellsters to choose between two settings a,a0while Bob uses a bit from the Bellsters
to choose between two different settings b,b0. Because we include 15 different time bins each trial, when certain settings are
chosen there is a significant probability in a given trial of Alice and Bob both detecting photons, but in different time bins.
Using conventional Bell inequalities, these detections would normally be considered a coincidence event even though they involve
unentangled photons from different photon pairs. To help limit the effect of these unwanted coincidences, we use a modified
Clauser-Horne (CH) inequality104 that accounts for the 15 individual time bins that a detection can take place in at either Alice
or Bob. During a trial if Alice (Bob) detects a photon in time bin i, we label the event iA(iB). If no detection is observed, then
the outcome is labelled with a 0Afor Alice or 0Bfor Bob. If two separate photon events are detected by either Alice or Bob in
the same trial, only the first bin is counted. The modified inequality is:
K=
n
X
i=1
P(iA,iB|ab)−
n
X
i=1
P(iA,iB|a0b0)−
n
X
i=1
P(0A,iB|a0b)−
n
X
i=1 X
j6=i
P(jA,iB|a0b)−
n
X
i=1
P(iA, 0B|ab0)−
n
X
i=1 X
j6=i
P(iA,jB|ab0)≤0
(7)
Here n= 15 for our experiment. The term P(iA,iB|ab) represents the probability that Alice and Bob both detect photons in
time bin i, given that Alice chooses setting aand Bob chooses setting b. The term P(iA,iB|a0b0) is the same, but for settings
a0and b0. This eliminates from the inequality the high probability of accidental coincidences where Alice and Bob, with joint
settings a0and b0, detect photons in different time bins (i6=j) during the same trial. The terms P(0A,iB|a0b) and P(iA, 0B|ab0)
correspond to cases where only one party detects a photon in a given trial. Finally, the P(jA,iB|a0b) and P(iA,jB|ab0) terms
correspond to trials where Alice and Bob both detect photons, but not in the same time bins.
To see that equation 7 is a valid Bell inequality, we note that if local realism holds then each term can be written as an
integral over hidden variables, λ. Then, because Alice and Bob are far enough apart, Alice’s measurement setting (SA) and
outcome (OA) can be factored from Bob’s measurement setting (SB) and outcome (OB):
P(Oa,Ob|SaSb) = ZP(Oa,Ob|SaSbλ)ρ(λ)dλ=ZP(Oa|Saλ)P(Ob|Sbλ)ρ(λ)dλ. (8)
Since the probability of some event, E, occurring is P(E)=1−P(¯
E), where P(¯
E) is the probability the event does not
occur, the two terms with double sums can be re-written, as
n
X
i=1 X
j6=i
P(jA,iB|a0b) =
n
X
i=1 ZP(iB|bλ)[1 −P(iA|a0λ)−P(0A|a0λ)]ρ(λ)dλ,
n
X
i=1 X
j6=i
P(iA,jB|ab0) =
n
X
i=1 ZP(iA|aλ)[1 −P(iB|b0λ)−P(0B|b0λ)]ρ(λ)dλ.
(9)
Now, since everything is just a sum over i, we can first pull the sum and then the integral out of all terms. A number of
terms cancel, leaving us with:
K=
n
X
i=1 ZP(iA|aλ)P(iB|bλ)−P(iA|a0λ)P(iB|b0λ)−P(iB|bλ) + P(iB|bλ)P(iA|a0λ)−P(iA|aλ) + P(iA|aλ)P(iB|b0λ)ρ(λ)dλ.
(10)
The fact that the four remaining probabilities, P(iA|aλ), P(iB|bλ), P(iA|a0λ), and P(iB|b0λ) are all bounded between 0 and 1
implies that the maximum value of each integrand is 0, following the arguments of104.
Using this inequality, we measure a Bell parameter of K= (1.70 ±0.20)x10−4, corresponding to an 8.7-σviolation of a
Bell inequality (under the assumptions of a normal distribution for the Bell parameter, and of each trial being independent
and identical). Table III contains the number of photons detected and the number of trials for each term in Equation 7.
We also analyzed the data from the experiment that used computer-based randomness, and obtained a Bell parameter of
K= (1.55 ±0.14)x10−4corresponding to an 11.2-σviolation a Bell inequality. The violation is larger because we performed
nearly twice as many trials with the computer-based random number generator, allowing us to obtain better statistics. Both of
these results constitute a strong rejection of local realism. A full record of the data, along with the code used to analyze it, can
be found at105.
It is also possible to carry out a hypothesis test to see how well a local-realistic theory could reproduce the correlations we
observed in our experiment. Such a test does not require assumptions about memory effects and the statistical distributions
of each trial’s outcomes. We devised the following analysis protocol before running the experiment. The first 5% of the data
was used for training purposes to estimate the rate of relevant events, given by terms in equation 8. From this, an estimate of
35
TABLE III. The number of photons detected for each of the terms in equation 7. Due to the large bias towards zeros in the bits
received from the Bellsters, it is necessary to normalize the counts by the number of trials conducted at each setting. A total of
40,559,990 trials were carried out over the course of the experiment. A second experiment 74,400,000 trials long that used only
unbiased random bits from a computer was run immediately afterwards.
P15
i=1 P(iA,iB|ab)P15
i=1 P(iA,iB|a0b0)P15
i=1 P(0A,iB|a0b)P15
i=1 Pj6=iP(jA,iB|a0b)P15
i=1 P(iA, 0B|ab0)P15
i=1 Pj6=iP(iA,jB|ab0)
Random bits from Bellsters
Events 20265 712 7475 143 8181 123
Trials 11126350 9202147 10125716 10125716 10105777 10105777
Random bits from computers
Events 33543 1677 13911 249 14589 228
Trials 18600599 18598891 18599346 18599346 18601164 18601164
the total number of remaining events was made. A stopping criteria, ncut , defined as 90% of the estimated remaining relevant
events was defined. Once ncut relevant events were processed the analysis was stopped, and the p-value was computed using a
binomial analysis of equation 7 (see103 for more details).
Our hypothesis test protocol was flawed, and failed to observe a violation. When we initially ran the protocol on our data
we obtained a p-value 3.3x10−70, with ncut = 30, 916 events. This is a much smaller p-value than expected. Looking more
closely at the data, we realized that there is an approximately 5% bias of excess zeros compared to ones submitted by the
Bellsters. Given that over 100,000 individuals from around the world independently submitted zeros and ones, such a large bias
was surprising. We do not have a definitive explanation for this, but we suspect it might be related to the majority of humans
being right-hand dominant. Most keyboards use the right hand to input a zero. On most specialized number pads, the zero
key is also substantially larger. For our setup the ab setting, which contributes to events that violate equation 7, occurs more
frequently than the other settings due to the bias. Since our hypothesis test protocol was devised under the assumption that all
the settings are equiprobable, we must correct our p-value to account for this large excess bias. After performing this correction,
we obtain a p-value of ≈1, and we are unable to reject the null hypothesis that local realism governs our experiment whose
random inputs were generated by humans. The data from the computer-based random number generator, however, had the
unbiased settings distribution required by our hypothesis test protocol. From this data set we obtained a p-value of 2.6x10−27
with ncut = 54,720, corresponding to a strong rejection of local realism.
The null result from the hypothesis test with human-based randomness does not mean that local realism governed the
experiment. The hypothesis test protocol we followed assumed that there was no bias in both Alice’s and Bob’s settings choices.
An improved protocol, for future experiments, would include a step that first estimates the bias from the training data in order
to determine the optimal Bell inequality to test. As long as there are only small deviations from this estimated bias (on the
order of <0.2%) over the remainder of the experiment, it would be possible to compute a rigorous p-value significantly smaller
than 1. Additionally, our measurement of the Bell parameter value is good evidence that local realism is not consistent with
the experimental correlations we observed. The Bell parameter is normalized by the total trials for each settings choice, and is
therefore insensitive to bias in the settings distribution. Under the assumptions that each trial was independent and identically
distributed and that the Bell parameter was normally distributed, the measured Bell parameter exceeds the maximum bound
predicted by local realism by a statistically significant amount. Even if these assumption are not true, it would take a local
realistic theory with a contrived distribution to appreciably lower this significance. For some applications, like using a loophole-
free Bell test to extract randomness, it is important to use a rigorous hypothesis testing framework to guard against a malicious
adversary who might be able to produce such contrived distributions to attack the system. However, one hopes that nature is
not so malicious when testing local realism.
We wanted to see if there was a difference between the results of a Bell test where humans chose the settings at Alice and
Bob versus a Bell test that used non-human random number generators. After accounting for the bias in the human inputs,
data from both the human-based input and the computer-based input were able to violate a Bell inequality.
102 F. Marsili, et al., Detecting single infrared photons with 93% system efficiency, Nature Photonics 7, 210 (2013).
103 L. K. Shalm, et al., Strong loophole-free test of local realism, Phys. Rev. Lett. 115, 250402 (2015).
104 J. F. Clauser, M. A. Horne, Experimental consequences of objective local theories, Phys. Rev. D 10, 526 (1974).
105 ”DOI placeholder for NIST Data.”.
