Light-matter entanglement over 50 km of optical fibre

Abstract

When shared between remote locations, entanglement opens up fundamentally new capabilities for science and technology. Envisioned quantum networks use light to distribute entanglement between their remote matter-based quantum nodes. Here we report on the observation of entanglement between matter (a trapped ion) and light (a photon) over 50 km of optical fibre: two orders of magnitude further than the state of the art and a practical distance to start building large-scale quantum networks. Our methods include an efficient source of ion–photon entanglement via cavity-QED techniques (0.5 probability on-demand fibre-coupled photon from the ion) and a single photon entanglement-preserving quantum frequency converter to the 1550 nm telecom C band (0.25 device efficiency). Modestly optimising and duplicating our system would already allow for 100 km-spaced ion–ion heralded entanglement at rates of over 1 Hz. We show therefore a direct path to entangling 100 km-spaced registers of quantum-logic capable trapped-ion qubits, and the optical atomic clock transitions that they contain.

Full text

ARTICLE OPEN
Light-matter entanglement over 50 km of optical fibre
V. Krutyanskiy
1
, M. Meraner
1,2
, J. Schupp
1,2
, V. Krcmarsky
1,2
, H. Hainzer
1,2
and B. P. Lanyon
1,2
When shared between remote locations, entanglement opens up fundamentally new capabilities for science and technology.
Envisioned quantum networks use light to distribute entanglement between their remote matter-based quantum nodes. Here we
report on the observation of entanglement between matter (a trapped ion) and light (a photon) over 50 km of optical fibre: two
orders of magnitude further than the state of the art and a practical distance to start building large-scale quantum networks. Our
methods include an efficient source of ion–photon entanglement via cavity-QED techniques (0.5 probability on-demand fibre-
coupled photon from the ion) and a single photon entanglement-preserving quantum frequency converter to the 1550 nm telecom
C band (0.25 device efficiency). Modestly optimising and duplicating our system would already allow for 100 km-spaced ion–ion
heralded entanglement at rates of over 1 Hz. We show therefore a direct path to entangling 100 km-spaced registers of quantum-
logic capable trapped-ion qubits, and the optical atomic clock transitions that they contain.
npj Quantum Information (2019) 5:72 ; https://doi.org/10.1038/s41534-019-0186-3
INTRODUCTION
Envisioned quantum networks
1
consist of distributed matter-
based quantum nodes, for the storage, manipulation and
application of quantum information, which are interconnected
with photonic links to establish entanglement between the nodes.
While the most ambitious form of a quantum network is a
collection of remote quantum computers, far simpler networks
with a handful of qubits at each node could already enable
powerful applications in quantum enhanced distributed sensing,
timekeeping, cryptography and multiparty protocols.
2
Entanglement has been achieved between two atoms in traps a
few 10 m apart,
3
between two ions in traps a few metres apart
4
and recently between two nitrogen-vacancy centres 1.3 km apart.
5
In these experiments, photon-matter entanglement is first
generated, then detection of one or two photons heralds remote
matter-matter entanglement (entanglement is ‘swapped’from
matter-light to matter-matter). A current goal is to significantly
scale up the distance over which quantum matter can be
entangled to a 100 km or more, which are practical internode
spacings to enable large-scale quantum networks.
Some key challenges to entangling matter over such distances are
now described. First, the aforementioned matter systems emit
photons at wavelengths that are strongly absorbed in optical
waveguides (such as optical fibre), limiting the internode distance to
a few kilometres. For example, in the present work 854 nm photons
are collected from a trapped atomic ion. While the ~3 dB per km
losses suffered by 854nm photons through state-of-the-art optical
fibre allows for few kilometre internode distances, transmission over
50 km of fibre would be 10
−15
. Single-photon quantum frequency
conversion to the telecom C band (1550nm) would offer a powerful
solution: this wavelength suffers the minimum fibre transmission
losses (~0.18 dB per km, yielding 10% transmission over 50 km) and
is therefore an ideal choice for a standard interfacing wavelength for
quantum networking. Photons from solid-state memories,
6
cold gas
memories,
7,8
quantum dots and nitrogen-vacancy centres
9
have
been converted to telecom wavelengths. Frequency conversion of
photons from ions has very recently been performed, including to
the telecom C band (without entanglement),
10
to the telecom O
band with entanglement over 80 m
11
and directly to an atomic
Rubidium line at 780 nm.
12
The use of photon conversion to extend
the distance over which light-matter and matter-matter entangle-
ment can be distributed has not previously been achieved.
A second challenge to long distance matter entanglement is to
preserve entanglement when such long photonic channels are
involved. Uncontrolled decoherence processes that act on the photon
as it travels along its path, and those that act on the quantum matter
during the photon travel time, can easily destroy entanglement. For
example, the entanglement-carrying photon signal, which attenuates
exponentially with distance in any lossy waveguide, can be
overwhelmed by added photon noise from the photon frequency
conversion process or dark counts of the photon detectors. The inter-
node photon travel time also imposes a minimum coherence time for
matter, which for e.g. 50 km of optical fibre is already significant at
250 μs (and 500 μs to allow for the classical signal of a successful
herald to return). Moreover, quantum networking applications require
distributed entanglement of a quality above certain thresholds, for
which the required matter coherence times and photon signal to
noise ratio are far more challenging.
A third challenge comes again from the photon travel time. The
shortest time required to entangle remote matter (or indeed light)
in two places is the light travel time between them. The 500 μs
wait time over 50 km of optical fibre yields a maximum attempt
rate of only 2 kHz: one must wait 500 μs to learn if an individual
attempt to distribute remote entanglement has been successful.
To achieve practical entanglement distribution rates in the face of
such a restriction, one can work on achieving a high probability for
individual attempts to succeed and (or) to run many attempts in
parallel (as discussed later).
Received: 29 March 2019 Accepted: 5 August 2019
1
Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, Technikerstr. 21A, 6020 Innsbruck, Austria and
2
Institut für
Experimentalphysik, Universität Innsbruck, Technikerstr. 25, 6020 Innsbruck, Austria
Correspondence: B. P. Lanyon (ben.lanyon@uibk.ac.at)
These authors contributed equally: V. Krutyanskiy, M. Meraner, J. Schupp
www.nature.com/npjqi
Published in partnership with The University of New South Wales

In this work, entanglement between a trapped-ion qubit and a
photon that has travelled over 50 km of optical fibre is achieved.
The quality of the entanglement is sufficiently high to allow for a
clear violation of a Bell inequality—as required for some of the
most challenging device-independent quantum network applica-
tions.
13
Furthermore, when modestly optimised, the achieved rate
is expected to allow for entanglement distribution between
100 km-spaced trapped ions at rates over 1 Hz. The paper is
organised as follows. First, there is a short motivation for quantum
networking trapped ions. Second, a brief overview of the
experimental methods is given, with much detail left for the
Supplementary Material. Third, the tomographically reconstructed
entangled state, of the ion qubit and photon polarisation qubit
after 50 km, is presented and the achieved fidelity, efficiency and
rate are analysed. Fourth, the ion qubit is shown to provide a
quantum information storage time (coherence time) of more than
20 ms, allowing for future entanglement distribution over
thousands of kilometers. Finally, the prospects for 100 km ion–ion
entanglement are presented as well as a path to significantly
increase the rate via multi-mode and hybrid quantum networking.
Trapped ions are particularly powerful systems to enable
quantum networking and the envisioned applications. For
example, a complete set of tools for deterministic universal
manipulation of quantum information encoded into registers of
trapped ions is readily available and of a quality near fault tolerant
thresholds,
14–16
as required for arbitrary distance quantum
networking via the quantum repeater approach.
17,18
Key quantum
networking functionalities have been demonstrated between ions
over a few meters, including remote state teleportation
19
and
multi-ion protocols.
20
Trapped ions are also some of the most
sensitive measurement probes yet developed. For example, many
ion species, including the one used in this work, contain optical
atomic clock transitions and therefore entangling them over
distance enables the ideas presented in
21,22
to be explored.
RESULTS
Our network node consists of a
40
Ca
+
ion in a radio-frequency
linear Paul trap with an optical cavity that enhances photon
collection on the 854 nm electronic dipole transition (Fig. 1). A
Raman laser pulse at 393 nm triggers emission, by the ion, of a
photon into the cavity via a bichromatic cavity-mediated
Raman transition (CMRT).
23
Two indistinguishable processes are
driven in the CMRT, each leading to the generation of a
cavity photon and resulting in entanglement between photon
polarisation and the electronic qubit state of the ion of the form
1=
ffiffiffi
2
pðDJ¼5=2;mj¼5=2;VþDJ¼5=2;mj¼3=2;HÞ, with horizontal (H)and
vertical (V) photon polarisation and two metastable Zeeman states
of the ion ðDJ;mjÞ, see Supplementary Fig. 3. The total measured
probability of obtaining an on-demand free-space photon out of
the ion vacuum chamber (entangled with the ion) is P
out
=0.5 ±
0.1 (Secction II, Supplementary material of this paper), enabled by
the novel low-loss cavity in our setup.
The CMRT yields an entangled state with a frequency-
degenerate photon qubit (the two polarisation components have
the same frequency to within the cavity linewidth
23
), providing a
significant benefit for long distance networking: the phase of the
light-matter entangled state does not depend on the time at
which the photon detection event occurs at a given distance from
the ion. Photon detection time fluctuates due to the intrinsic finite
temporal extent of the photon wavepacket and in the case of
optical path length changes, which could be significant over tens
of kilometres of deployed optical fibre. Our photons are generated
over several tens of microseconds, with a corresponding
bandwidth of tens of kilohertz. This unusually narrow bandwidth
allows for strong frequency filtering, which we exploit in the
photon conversion process and could have further benefits in
future deployed networks, e.g to enable co-propagating classical
and quantum light. Furthermore, the corresponding photon
coherence-length is potentially thousands of metres, allowing
for essentially path-length-insensitive entanglement swapping
between remote ions via Hong-Ou-Mandel interference.
4,24,25
Single-mode fibre-coupled photons from the ion are injected
into a polarisation-preserving photon conversion system (pre-
viously characterised using classical light
26
). In summary, a χ
(2)
optical nonlinearity is used to realise difference frequency
generation, whereby the energy of the 854 nm photon is reduced
by that of a pump-laser photon at 1902 nm, yielding 1550 nm.
Two commercially available free-space and crossed PPLN ridge
waveguide crystals are used, one to convert each polarisation, in a
self-stable polarisation interferometer. The total fibre-coupled
device conversion efficiency here is 25 ± 0.02%, for an added
white noise of 40 photons per second, within the filtering
bandwidth of 250 MHz centred at 1550 nm. As discussed in,
26
the
854 nm line in
40
Ca
+
is almost unique amongst trapped-ion
transitions in its potential for low-noise, highly-efficient single-step
frequency conversion to the telecom C band.
Following conversion, the telecom photon is injected into a
50.47 km ‘SMF28’single-mode fibre spool with 0.181 dB per km
loss (10.4 ± 0.5% measured total transmission probability). The
spool is not actively stabilised. Polarisation dynamics in an
unspooled fibre could be actively controlled using methods
developed in the field of quantum cryptography (e.g.,
27
). Finally,
free-space projective polarisation analysis is performed and the
photon is detected using a telecom solid-state photon detector
with an efficiency of 0.10 ± 0.01 and free-running dark count rate
Fig. 1 Simplified experiment schematic. From left to right: a single atomic ion (red sphere) in the centre of a radio-frequency linear Paul trap
(gold electrodes) and a vacuum anti-node of an optical cavity. A Raman laser pulse triggers emission of an 854 nm photon into the cavity,
which exits to the right. The photon, polarisation-entangled with two electronic qubit states of the ion (two Zeeman states of the D
J
=5/2
manifold, not shown), is then wavelength-converted to 1550 nm using difference frequency generation involving ridge-waveguide-integrated
periodically-poled lithium niobate (PPLN) chips and a strong (~1 W ) pump laser at 1902 nm.
26
The photon then passes through a 50 km single-
mode fibre spool, is filtered with a 250 MHz bandwidth etalon (SF) to reduce noise from the conversion stage,
26
and is polarisation-analysed
using waveplates, a polarising beam splitter (PBS) and a solid-state single photon counting module (SPCM, InGaAs ID230 from IDQuantique).
The electronic state of the ion is measured (not shown), conditional on the detection of a photon. Additional photon conversion filters are not
shown.
26
For further details see, Supplementary material of this paper section I
V. Krutyanskiy et al.
2
npj Quantum Information (2019) 72 Published in partnership with The University of New South Wales
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of 2 counts per second (cps). Measurement of the ion-qubit state
is performed conditional on the detection of a 50 km photon
within a 30 μs time window: the Zeeman ion qubit is mapped into
the established
40
Ca
+
optical quadrupole clock qubit
28
via laser
pulses at 729 nm, followed by standard fluorescence state
detection (see Methods).
Quantum state tomography is performed to reconstruct the two-
qubit (ion qubit and photon polarisation qubit) state, Supplemen-
tary material of this paper section III. The 247 μs photon travel time
through the fibre limits the maximum attempt rate for generating a
photon from the ion to 4 kHz (2 kHz if the fibre was stretched out
away from our ion to force an additional delay for the classical
signal ‘photon click’to return). Here, until photon detection occurs,
photon generation is (Raman laser pulses are) performed every
453 μs, yielding an attempt rate of 2.2 kHz. For the complete
experimental sequence see Methods. All error bars on quantities
derived from the tomographically-reconstructed states (density
matrices) are based on simulated uncertainties due to finite
measurement statistics (see Supplementary Material section III).
A strongly entangled ion–photon state is observed (Fig. 2)over
50 km, quantified by a concurrence
29
C=0.75 ± 0.05 and state
fidelity F
m
=0.86 ± 0.03 with a maximally entangled state (C=1).
Simulating a CHSH Bell inequality test
30
on our tomographic data
yields a value of 2.304 ± 0.125, thereby exceeding the classical bound
(of 2) by 2.4 standard deviations. Using a shorter detection window
(first 2/3 of the full photon wavepacket) increases the signal to noise
ratio and yields F
m
=0.90 ± 0.03 and CHSH Bell inequality violation
by 4.8 standard deviations at the expense of an efficiency decrease
of only 10%. The quality of our light-matter entangled state therefore
surpasses this stringent threshold for its subsequent application.
For a detailed analysis of the sources of infidelity in the
entangled state see, Supplementary material of this paper section
IV; here now is a short summary. In a second experiment, the
telecom entangled state is reconstructed right after the conversion
stage (without the 50 km spool), yielding F
m
=0.92 ± 0.02. The
drop in fidelity when adding the 50 km spool can, to within
statistical uncertainty, be entirely explained by our telecom photon
detector dark counts (2cps). In a third experiment, the 854 nm
entangled state is reconstructed right out of the vacuum chamber
(without conversion), yielding F
m
=0.967 ± 0.006. The observed
drop in fidelity through the conversion stage alone is dominated
by a drop in photon signal to noise signal. Here the noise consists
of comparable rates of telecom detector dark counts and
conversion noise (caused by Anti-Stokes Raman scattering of the
pump laser
26
) and the signal is reduced by the finite conversion
setup efficiency and the lower telecom detector’sefficiency
compared to the 854 nm one. The infidelity in the 854 nm
photon-ion entangled state is consistent with that achieved in.
23
The total probability that a Raman pulse led to the detection of
a photon after 50 km was P=5.3 × 10
−4
, which given an attempt
rate of 2.2 kHz yielded a click rate of ≈1 cps. Photon loss
mechanisms in our experiment are discussed in, Supplementary
material of this paper section II. In summary, the 50 km fibre
transmission (0.1) and our current telecom detector efficiency (0.1)
limit the maximum click probability to P=0.01. The majority of
other losses are in passive optical elements, and could largely be
eliminated by e.g. more careful attention to coupling into optical
fibres and photon conversion waveguides. In combination with
state-of-the-art telecom detectors (e.g. Scontel recently supplied
us superconducting nanowire detectors providing 0.8 cps dark
count rate and 77% efficiency according to the company’s
calibration), a total 50 km efficiency of P≈0.01 would be expected
and a corresponding click rate of ≈20 cps.
One of the functions played by matter in a quantum network is
as a memory to store established entanglement, while entangle-
ment is being made or processed in other parts of the network.
Decoherence processes in the matter qubit will limit the distance
over which it is possible to distribute quantum entanglement (the
distance a photon could possibly travel in the ‘coherence time’of
the matter qubit). In our 50 km experiment, the ion qubit is
already stored for the 250 μs photon travel time through the
50 km fibre, with no statistically significant reduction in the
ion–photon entanglement quality (this was achieved by installing
a mu-metal shield around the ion-trap vacuum chamber to
attenuate ambient magnetic field fluctuations).
Additional tomographic measurements are performed to see for
how long ion–photon entanglement could be stored in our ion-
trap network node before decoherence in the ion-qubit would
destroy it. Specifically, state tomography is performed for increas-
ing delays introduced between measurements of the telecom
photon polarisation state (0 km fibre travel distance) and measure-
ments of the state of the ion-qubit. This is equivalent to introducing
an additional storage time for the ion-qubit. The results show that
strong entanglement is still present after 20 ms wait time (F
m
=
0.77 ± 0.04, C=0.57 ± 0.08), the longest wait time employed. This
already opens up the possibility of distributing entanglement over
several thousands of kilometers and the time to perform hundreds
of single and multi-qubit ion quantum logic gates.
31
A dominant source of decoherence of our ion-qubit are
uncontrolled fluctuating energy-level shifts due to intensity
fluctuations of the 806 nm laser field used to lock the cavity
around the ion. Further attention to minimising the absolute size
of these fluctuations should lead to entanglement storage times
of more than ≈100 ms and therefore the possibility to distribute
entanglement to the other side of the earth. Beyond this, the ion-
qubit could be transferred to hyperfine clock transitions within
different co-trapped ion species that offer coherence times of
many seconds and longer.
32
DISCUSSION
The rates for future 100 km-spaced photon-detection heralded
ion–ion entanglement using our methods are now discussed (see
Fig. 3). A modestly optimised version of our experimental system
in this work is now considered (see dashed box in Fig. 3), that
achieves an on-demand detected 50 km photon click probability
of P=0.01 and operates at an attempt rate of R=2 kHz (the two-
way light travel time). By duplicating our optimised system (Fig. 3),
and following a two-photon click heralding scheme,
24
the
probability of heralding a 100 km-spaced ion–ion entangled state
would be H2¼1
2P2¼5´105, at an average click rate of H
2
×R=
0.1 cps (comparable with the first rates achieved over a few
meters
33
of 0.03 cps. Following instead a one-photon click
Time (μs)
260 280 300 320 340 360 380
0
0.3
Photon click
probability (x10-4)
Fig. 2 Observation of ion-photon entanglement over 50 km of
optical fibre. (i) 2D red bar chart: histogram of photon detection
times (photon wavepacket in dashed box), following the generation
of an 854 nm photon with a 30 μs Raman laser pulse (R) ≈250 μs
earlier, repeated at 2.2 kHz. Ion–photon state tomography is
performed for photon detection events recorded in the dashed
box (total contained probability P=5.3 × 10
−4
). (ii) 3D bar chart:
absolute value of experimentally-reconstructed density matrix of the
telecom photonic polarisation qubit (Hand Vare Horizontal and
Vertical, respectively) and ion-qubit state (0¼DJ¼5=2;mj¼3=2,
1¼DJ¼5=2;mj¼5=2)
V. Krutyanskiy et al.
3
Published in partnership with The University of New South Wales npj Quantum Information (2019) 72

heralding scheme,
24
the probability of heralding a 100 km-spaced
ion–ion entangled state would be H
1
=2P× 0.1 =0.002, at an
average click rate of H
1
×R=4 cps, where 0.1 is the reduced
photon generation probability at each node (as required for this
scheme). The factor 40 improvement (H
1
/H
2
) of the one-photon
scheme over the two-photon scheme comes at the expense of the
need to interferometrically stabilise the optical path length across
the 100 km network.
An approach to significantly increase the remote entanglement
heralding rate is multi-mode quantum networking, where many
photons are sent, each entangled with different matter qubits. In
this way, of running many such processes in parallel, the
probability of at least one successful heralding event occurring
can be made arbitrarily high. In our setup, for example, multiple
ions can be trapped and it may be possible to produce a train of
photons, each entangled with a different ion. In this case, a higher
rate of photon production can be employed, as the time between
photons in the train is not limited by the light travel time.
Furthermore, multi-mode networking could be realised using
inhomogenously broadened ensemble based solid-state quantum
memories.
34
Such memories could be quantum-networked with
ions via a photon conversion interface
35
to form a powerful hybrid
system for long distance quantum networking.
The 50 km photon in our experiments is entangled with the
729 nm optical-qubit clock transition in
40
Ca
+
, over which a
fractional frequency uncertainty of 1 × 10
−15
has been achieved
(comparable with the Cs standard).
36
Furthermore,
40
Ca
+
can be
co-trapped with Al
+
,
37
which contains a clock transition for which
a fractional systematic frequency uncertainty at the 1 × 10
−18
level
was recently achieved.
38,39
Transfer of the remote
40
Ca
+
entanglement to a co-trapped Al
+
ion could be done via quantum
logic techniques.
39,40
As such, our work provides a direct path to
realise entangled networks of state-of-the-art atomic clocks over
large distances.
21
Entangling clocks provides a way to perform
more sensitive measurements of their average ticking frequen-
cies
21
and to overcome current limits to their synchronisation.
22
METHODS
Trapped ion node
We use a 3D radio-frequency linear Paul trap with a DC endcap to ion
separation of 2.5 mm and ion to blade distance of 0.8 mm. The trap
electrodes are made of titanium, coated with gold and are mounted on
Sapphire holders. The trap drive frequency is 23.4 MHz. The radial secular
frequencies are ω
x
≈ω
y
=2π× 2.0 MHz, split by approximately 10 kHz and
the axial frequency is ω
z
=2π× 0.927 MHz. Atoms are loaded from a
resistively heated atomic oven and ionised via a two photon process
involving 375 and 422 nm laser light.
The optical cavity around the ion is near-concentric with a length l=
19.9057 ± 0.0003 mm and radii of curvature ROC =9.9841 ± 0.0007 mm,
determined from simultaneous measurements of the free spectral range
(FSR) and higher-order TEM mode spacing (assuming identical mirror
geometries).
41
From this we calculate an expected cavity waist of ω
0
=
12.31 ± 0.07 μm and a maximum ion-cavity coupling rate of g
max
=2π×
1.53 ± 0.01 MHz. The finesse of the cavity (at 854 nm) is
F¼2π
L¼54000 ± 1000, with the total cavity losses L¼T1þT2þL1þ2¼
116 ± 2 ppm, determined from measurements of the cavity ringdown time.
This gives the cavity linewidth 2κ=2π× 140 ± 3 kHz, κbeing the half-
width at half maximum. Taking into account the spontaneous scattering
rate of the P
3/2
state of the ion (γ=2π× 11.45 MHz, half-width) the
expected cooperativity is C¼g2
max
2κγ ¼1:47 ± 0:03.
The transmission T
1,2
of our cavity mirrors was measured to be T
1
=
2.2 ± 0.3 ppm, T
2
=97 ± 4 ppm, that yields expected probability of
extracting a photon from the cavity of Pmax
out ¼T2=ðT1þT2þL1þ2Þ¼
0:83 ± 0:03 (polishing of the mirror substrates done by Perkins Precision
Development, Boulder (Colorado), coating done by Advanced Thin Films).
The optical cavity axis is close to perpendicular to the principle ion trap axis
(~5° difference). A magnetic field of 4.22 G is applied perpendicular to the
cavity axis and at an angle of 45° to the principal ion trap axis (Supplementary
Fig. 1). The Raman photon generation beam is circularly polarised and parallel
to the magnetic field (to maximise the coupling on the relevant dipole
transition SJ¼1=2;mj¼1=2$PJ¼3=2;mj¼3=2, see Supplementary Fig. 3).
Pulse sequence for 50 km experiment
First, a 30 μs‘initialisation’laser pulse at 393 nm is applied, measured by a
photodiode in transmission of the ion-trap chamber, which allows for
intensity stabilisation of the subsequent 393 nm photon generation Raman
pulse via a sample and hold system. The initialisation pulse is followed by a
1500 μs Doppler cooling pulse. Next, a loop starts in which single photons
are generated (see Supplementary Fig. 2). This loop consists of an additional
Doppler cooling pulse (50 μs), optical pumping to the S¼SJ¼1=2;mj¼1=2
state via circularly polarised 397 nm ‘sigma’laser light (60 μs), and a 393 nm
photon generation Raman pulse (30 μs). This is followed by a wait time for
the photon to travel through the 50 km fibre and a subsequent photon
detection window. This sequence loops until a photon is detected.
In the case of a photon detection (detector ‘click’), the state of the ion is
measured. To perform an ion state measurement, the D0¼DJ¼5=2;mj¼5=2
electron population is first mapped to the S¼SJ¼1=2;mj¼1=2state via a
729 nm πpulse (Supplementary Figs. 2 and 3). That is, the D-manifold qubit
is mapped into an optical qubit (with logical states S¼SJ¼1=2;mj¼1=2and
D¼DJ¼5=2;mj¼3=2). In order to measure which of these states the electron
is in, the standard electron shelving technique is used. We perform this
measurement for a ‘detection time’(397 nm photon collection time) of
1500 μs, which is sufficient to distinguish bright (scattering) and dark (non-
scattering) ions with an error of less than 1%. The aforementioned process
implements a projective measurement into the eigenstates of the σ
z
basis
(Pauli spin-1/2 operator).
To perform measurements in other bases e.g σ
x
(σ
y
), as required for full
quantum state tomography, an additional π/2 pulse on the Smj¼1=2to
Dmj¼3=2with a 0 (π/2) phase is applied after the πpulse and before the
397 nm pulse, to rotate the ion-qubit measurement basis. The scheme of
the experimental sequence is given in Supplementary Fig. 2.
State characterisation
To reconstruct the ion–photon state, a full state tomography of the two-
qubit system is performed. On the photon polarisation qubit side, the state
is projected to one of 6 states (horizontal, vertical, diagonal, anti-diagonal,
right circular and left circular) by waveplates and a polariser. This is
equivalent to performing projective measurements in three bases
described by the Pauli spin-1/2 operators. For example, horizontal and
vertical are the eigenstates of the Pauli σ
z
operator. On the ion qubit side,
measurement is performed in the three Pauli bases as described in the
previous section. From these measurements’outcomes probabilities we
reconstruct the 2-qubit state density matrix by linear search with
subsequent Maximum Likelihood method.
42
The values of fidelity,
concurrence and other measures presented in the Results section are
calculated using reconstructed density matrices for each of the experi-
ments. The error bars for all quantities provided in the Results section
A1
D1 D2
QFC
B1B2
A2
QFC
QFC
854 nm 1550 nm
50 km
BS
100 km
This work
Q. Node Q. Node
QFC
Fig. 3 Path to 100 km matter-matter entanglement. This work:
quantum frequency conversion (QFC) converts a photon, emitted
on-demand from and entangled with an ion qubit (A
1
) in node A, to
the telecom C band at 1550 nm. The photon then travels through
50 km of optical fibre before detection (D1 or D2). Future work:
duplicating the system, interfering the two photonic channels on a
beamsplitter (BS). Single or two photon detection heralds the
projection of ions A
1
and B
1
into an entangled state.
24
Deterministic
intra-node quantum logic and measurement between e.g. B
1
and B
2
and A
1
and A
2
can swap the entanglement over larger distances
(quantum repeater). Additional qubits in nodes are available for
entanglement purification. Nodes could as well contain solid-state
memories,
35
NV centres
9
or neutral atoms.
7,8
V. Krutyanskiy et al.
4
npj Quantum Information (2019) 72 Published in partnership with The University of New South Wales

represent one standard deviation of distribution of these quantities over
randomised set of data following the Monte-Carlo approach, for more
details see Supplementary material of this paper section III.
DATA AVAILABILITY
The data and code that support the findings of this study are available from the
corresponding author upon reasonable request.
ACKNOWLEDGEMENTS
We thank the staff at IQOQI Innsbruck; Rainer Blatt for providing encouragement,
laboratory space and the environment and group support in which to develop our work;
Daniel Heinrich, Klemens Schüppert, Tiffany Brydges, Christine Maier and Tracy Northup
for their support. This work was supported by the START prize of the Austrian FWF project
Y 849-N20, the Army Research Laboratory Center for Distributed Quantum Information via
the project SciNet under Cooperative Agreement Number W911NF-15-2-0060, the
Institute for Quantum Optics and Quantum Information (IQOQI) of the Austrian Academy
Of Sciences (OEAW) and the European Union’s Horizon 2020 research and innovation
programme under grant agreement No 820445 and project name ‘Quantum Internet
Alliance’. The European Commission is not responsible for any use that may be made of
the information this paper contains.
AUTHOR CONTRIBUTIONS
All authors contributed to the design, development and characterisation of the
experimental systems. In particular, J.S. focused on the ion trap and optical cavity,
M.M. on the photon conversion system, V. Krc. on the ion trap, H.H. on laser
frequency stabilisation and V. Kru. and B.P.L. on all aspects. Experimental data taking
was done by V. Kru., V. Krc., M.M. and J.S. Data analysis and interpretation was done
by V. Kru., J.S., M.M. and B.P.L. All authors contributed to the paper writing. The
project was conceived and supervised by B.P.L.
ADDITIONAL INFORMATION
Supplementary information accompanies the paper on the npj Quantum
Information website (https://doi.org/10.1038/s41534-019-0186-3).
Competing interests: The authors declare no competing interests.
Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims
in published maps and institutional affiliations.
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