[Show abstract][Hide abstract] ABSTRACT: Measurement scenarios containing events with relations of exclusivity represented by pentagons, heptagons,
nonagons, etc., or their complements are the only ones in which quantum probabilities cannot be described
classically. Interestingly, quantum theory predicts that the maximum values for any of these graphs cannot be
achieved in Bell inequality scenarios. With the exception of the pentagon, this prediction remained experimentally unexplored. Here we test the quantum maxima for the heptagon and the complement of the heptagon using three- and five-dimensional quantum states, respectively. In both cases, we adopt two different encodings: linear transverse momentum and orbital angular momentum of single photons. Our results exclude maximally noncontextual hidden-variable theories and are in good agreement with the maxima predicted by quantum theory.
Physical Review A 09/2015; 92(3):032126. DOI:10.1103/PhysRevA.92.032126 · 2.81 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The interpretation of quantum theory is one of the longest-standing debates
in physics. Type-I interpretations see quantum probabilities as determined by
intrinsic properties of the world. Type-II interpretations see quantum
probabilities as not directly dealing with intrinsic properties of the world
but with relational experiences between an observer and the world. It is
usually believed that deciding between these two types cannot be made simply on
purely physical grounds but it requires an act of metaphysical judgement. Here
we show that, although the problem is undecidable within the framework of
quantum theory, it is decidable, under some assumptions, within the framework
of thermodynamics. We prove that type-I interpretations are incompatible with
the following assumptions: (i) the decision of which measurement is performed
on a quantum system can be made independently of the system, (ii) a quantum
system has limited memory, and (iii) Landauer's principle is valid. We consider
an ideal experiment in which an individual quantum system is submitted to a
sequence of quantum projective measurements that leave the system in pure
quantum states. We show that in any type-I interpretation satisfying (i)-(iii)
the system must reset its internal state, which implies that a minimum amount
of heat per measurement has to be dissipated into the system's environment. We
calculate a lower bound to the heat dissipated per measurement assuming that
the measurements are chosen from a set of size $2^n$. Then, we show that this
lower bound becomes infinite in the limit of $n$ tending to infinity. This
leads to the conclusion that either type-I interpretations are untenable or at
least one of the assumptions (i)-(iii) has to be abandoned.
[Show abstract][Hide abstract] ABSTRACT: Quantum nonlocality can be revealed "via local contextuality" in qudit-qudit
entangled systems with $d > 2$, that is, through the violation of inequalities
containing only Alice-Bob correlations that admit a local description, and
Alice-Alice correlations (between the results of sequences of measurements on
Alice's subsystem) that admit a local (but contextual) description. A
fundamental question to understand the respective roles of entanglement and
local contextuality is whether nonlocality via local contextuality exists when
the parties have only qubit-qubit entanglement. Here we respond affirmatively
to this question. This result further clarifies the connection between
contextuality and nonlocality and opens the door for observing nonlocality via
local contextuality in actual experiments.
[Show abstract][Hide abstract] ABSTRACT: Device-independent quantum communication will require a loophole-free violation of Bell inequalities.
In typical scenarios where line of sight between the communicating parties is not available, it is convenient
to use energy-time entangled photons due to intrinsic robustness while propagating over optical fibers. Here
we show an energy-time Clauser-Horne-Shimony-Holt Bell inequality violation with two parties separated
by 3.7 km over the deployed optical fiber network belonging to the University of Concepción in Chile.
Remarkably, this is the first Bell violation with spatially separated parties that is free of the postselection
loophole, which affected all previous in-field long-distance energy-time experiments. Our work takes a
further step towards a fiber-based loophole-free Bell test, which is highly desired for secure quantum
communication due to the widespread existing telecommunication infrastructure.
[Show abstract][Hide abstract] ABSTRACT: Contextuality is a fundamental feature of quantum theory and a necessary
resource for quantum computation and communication. It is therefore important
to investigate how large can contextuality be in quantum theory. Contextuality
witnesses can be expressed as a sum $S$ of $n$ probabilities, such that $1 \le
\alpha < \vartheta \le n$ are, respectively, the maximum of $S$ for
noncontextual theories and for the theory under consideration. A theory allows
for absolute maximal contextuality if it has scenarios in which
$\vartheta/\alpha$ tends to $n$. Here we show that quantum theory allows for
absolute maximal contextuality despite what is suggested by the examination of
the quantum violations of Bell and noncontextuality inequalities considered in
the past. Our proof is not constructive and does not single out explicit
scenarios. Nevertheless, we identify scenarios in which quantum theory allows
for almost absolute maximal contextuality.
[Show abstract][Hide abstract] ABSTRACT: There is a tension in quantum theory between the existence of a widely
accepted way to axiomatize the theory and the lack of similarly accepted
intuitive principles from which the theory can be derived. This tension is
present at the very definition of what measurements are admissible. The usual
assumption is that all measurements which do not produce negative probabilities
are valid measurements. However, besides simplicity, there is no conceptional
reason for such an assumption. Here we show that this assumption leads to a
very particular prediction that can be experimentally tested: in certain
situations, the number of outcomes of a measurement is, by itself, a quantum
phenomenon. For reaching this conclusion, we consider minor modifications of
quantum theory in which all measurements are produced from quantum measurements
with a limited number of outcomes and classical measurements, and show that any
of these modifications is accessible to falsification by particular
high-precision Bell-type experiments. Our analysis reveals that the results of
previous experiments provide evidence that nature cannot be explained with the
simplest of these modifications in which all measurements are essentially
quantum dichotomic. This supports standard quantum theory versus a natural and
almost indistinguishable alternative, but leaves as an open challenge to
perform experiments which allow us to exclude other alternatives such as
essentially trichotomic quantum theories and more general dichotomic theories.
[Show abstract][Hide abstract] ABSTRACT: Device-independent (DI) quantum communication will require a loophole-free
violation of Bell inequalities. In typical scenarios where line-of-sight
between the communicating parties is not available, it is convenient to use
energy-time entangled photons due to intrinsic robustness while propagating
over optical fibers. Here we show an energy-time Clauser-Horne-Shimony-Holt
Bell inequality violation with two parties separated by 3.7 km over the
deployed optical fiber network belonging to the University of Concepci\'on in
Chile. Remarkably, this violation is free of the post-selection loophole
affecting all previous in-field long-distance energy-time experiments. Our work
takes a further step towards a fiber-based loophole-free Bell test, which is
highly desired for secure quantum communication due to the widespread existing
telecommunication infrastructure.
[Show abstract][Hide abstract] ABSTRACT: Clock synchronization for nonfaulty processes in multiprocess networks is indispensable for a variety of technologies. A reliable system must be able to resynchronize the nonfaulty processes upon some components failing causing the distribution of incorrect or conflicting information in the network. The task of synchronizing such networks is related to Byzantine agreement (BA), which can classically be solved using recursive algorithms if and only if less than one-third of the processes are faulty. Here we introduce a nonrecursive quantum algorithm, based on a quantum solution of the detectable BA, which achieves clock synchronization in the presence of arbitrary many faulty processes by using only a single quantum system.
[Show abstract][Hide abstract] ABSTRACT: We solve the problem of whether a set of quantum tests reveals
state-independent contextuality and use this result to identify the simplest
set of minimal dimension. We also show that identifying state-independent
contextuality graphs [R. Ramanathan and P. Horodecki, Phys. Rev. Lett. 112,
040404 (2014)] is not sufficient for revealing state-independent contextuality.
[Show abstract][Hide abstract] ABSTRACT: Contextuality is a fundamental property of quantum theory and a critical resource for quantum computation. Here, we experimentally observe the arguably cleanest form of contextuality in quantum theory [A. Cabello et al., Phys. Rev. Lett. 111, 180404 (2013)] by implementing a novel method for performing two sequential measurements on heralded photons. This method opens the door to a variety of fundamental experiments and applications.
[Show abstract][Hide abstract] ABSTRACT: We show that, for general probabilistic theories admitting sharp measurements, the exclusivity principle together with two assumptions exactly singles out the Tsirelson bound of the Clauser-Horne-Shimony-Holt Bell inequality.
Physical Review A 12/2014; 90(6). DOI:10.1103/PhysRevA.90.062125 · 2.81 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Quantum $n$-body correlations violate inequalities for nonlocal theories in
which arbitrary correlations are allowed within any strict subset of bodies
while only local correlations are allowed between the subsets. Violations of
these inequalities have been recently observed up to $n=6$. An important
question is why the universe is exactly as genuinely $n$-body nonlocal as
predicted by quantum theory, but not more or less. Here we prove that, for any
$n>2$, the exclusivity principle and two assumptions (namely, independence of
remote experiments and existence of a joint probability distribution for
certain measurements), give, for general probabilistic theories, the same
genuinely $n$-body nonlocality found in quantum theory.
[Show abstract][Hide abstract] ABSTRACT: Random numbers are essential for a wide range of applications, including
cryptography, financial security, and digital rights management. However,
producing random numbers from a finite state machine, such as a classical
computer, is impossible. One alternative is to use quantum random number
generators (QRNG), which explore unpredictable results of quantum phenomena to
extract a string of random bits. Unfortunately, however, commercial QRNGs have
also to rely on assumptions on the internal workings of its devices.
"Device-independent" QRNGs are nevertheless possible, but are impractical since
they require Bell-inequality violations free of the detection loophole. Here,
we introduce a new protocol for quantum randomness extraction which works even
in the case of very low detection efficiency, and where no internal device
description is needed. The method is based on a new tensor-like indicator of
randomness, and there is only one assumption: that the dimension of the
prepared-and-measured quantum system is upper bounded, as in the
semi-device-independent (SDI) paradigm. We implement the protocol using weak
coherent states and standard single-photon detectors. Our results pave the way
towards a second generation of practical and more secure QRNGs.
[Show abstract][Hide abstract] ABSTRACT: Kochen-Specker (KS) sets are key tools for proving some fundamental results in quantum theory
and also have potential applications in quantum information processing. However, so far, their intrinsic
complexity has prevented experimentalists from using them for any application. The KS set requiring the
smallest number of contexts has been recently found. Relying on this simple KS set, here we report an input
state-independent experimental technique to certify whether a set of measurements is actually accessing a
preestablished quantum six-dimensional space encoded in the transverse momentum of single photons.
[Show abstract][Hide abstract] ABSTRACT: For eight-dimensional quantum systems there is a Kochen-Specker (KS) set of 40 quantum yes-no tests that is related to the Greenberger-Horne-Zeilinger (GHZ) proof of Bell's theorem. Here we experimentally implement this KS set using an eight-dimensional Hilbert space spanned by the transverse momentum of single photons. We show that the experimental results of these tests violate a state-independent noncontextuality inequality. In addition, we show that, if the system is prepared in states that are formally equivalent to a three-qubit GHZ and W states, then the results of a subset of 16 tests violate a noncontextuality inequality that is formally equivalent to the three-party Mermin's Bell inequality, but for single eight-dimensional quantum systems. These experimental results highlight the connection between quantum contextuality and nonlocality for eight-dimensional quantum systems.
Physical Review A 07/2014; 90(1):012119. DOI:10.1103/PhysRevA.90.012119 · 2.81 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Non-contextuality (NC) and Bell inequalities can be expressed as bounds
$\Omega$ for positive linear combinations $S$ of probabilities of events, $S
\leq \Omega$. Exclusive events in $S$ can be represented as adjacent vertices
of a graph called the exclusivity graph of $S$. In the case that events
correspond to the outcomes of quantum projective measurements, quantum
probabilities are intimately related to the Gr\"otschel-Lov\'asz-Schrijver
theta body of the exclusivity graph. Then, one can easily compute an upper
bound to the maximum quantum violation of any NC or Bell inequality by
optimizing $S$ over the theta body and calculating the Lov\'asz number of the
corresponding exclusivity graph. In some cases, this upper bound is tight and
gives the exact maximum quantum violation. However, in general, this is not the
case. The reason is that the exclusivity graph does not distinguish among the
different ways exclusivity can occur in Bell-inequality (and similar)
scenarios. An interesting question is whether there is a graph-theoretical
concept which accounts for this problem. Here we show that, for any given
$N$-partite Bell inequality, an edge-coloured multigraph composed on $N$
single-colour graphs can be used to encode the relationships of exclusivity
between each party's parts of the events. Then, the maximum quantum violation
of the Bell inequality is exactly given by a refinement of the Lov\'asz number
that applies to these edge-coloured multigraphs. We show how to calculate upper
bounds for this number using a hierarchy of semi-definite programs and
calculate upper bounds for $I_3$, $I_{3322}$ and the three bipartite Bell
inequalities whose exclusivity graph is a pentagon. The multigraph-theoretical
approach introduced here may remove some obstacles in the program of explaining
quantum correlations from first principles.
Journal of Physics A Mathematical and Theoretical 07/2014; 47(42). DOI:10.1088/1751-8113/47/42/424021 · 1.58 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We show that the exclusivity principle exactly singles out the Tsirelson
bound of the Clauser-Horne-Shimony-Holt Bell inequality. The proof is
surprisingly simple and does not require an infinite universe.
[Show abstract][Hide abstract] ABSTRACT: Several studies in recent years have demonstrated that upper-division students struggle with the mathematics of thermodynamics. This paper presents a task analysis based on several expert attempts to solve a challenging mathematics problem in thermodynamics. The purpose of this paper is twofold. First, we highlight the importance of cognitive task analysis for understanding expert performance and show how the epistemic games framework can be used as a tool for this type of analysis, with thermodynamics as an example. Second, through this analysis, we identify several issues related to thermodynamics that are relevant to future research into student understanding and learning of the mathematics of thermodynamics.
[Show abstract][Hide abstract] ABSTRACT: We show that correlations between the detector positions at the two-photon Young interference plane exhibit contextual behavior. Contextuality is demonstrated by showing the violation of the n-cycle noncontextuality inequalities [M. Araújo et al., Phys. Rev. A 88, 022118 (2013)] for any even number n of observables ranging from 4 to 14. These violations exclude noncontextual hidden-variable theories as an explanation of the conditional two-photon Young pattern. Unlike recent contextuality experiments, ours is free of the compatibility loophole.
Physical Review A 05/2014; 89. DOI:10.1103/PhysRevA.89.052106 · 2.81 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: An important problem in quantum information processing is the certification of the dimension of quantum systems without making assumptions about the devices used to prepare and measure them, that is, in a device-independent manner. A crucial question is whether such certification is experimentally feasible for high-dimensional quantum systems. Here we experimentally witness in a device-independent manner the generation of six-dimensional quantum systems encoded in the orbital angular momentum of single photons and show that the same method can be scaled, at least, up to dimension 13.