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Teleportation Systems Towards a Quantum Internet
Raju Valivarthi,1, 2 Samantha Davis,1, 2 Cristián Peña,1, 2, 3
Si Xie,1, 2 Nikolai Lauk,1, 2 Lautaro Narváez,1, 2
Jason P. Allmaras,4 Andrew D. Beyer,4 Yewon Gim,2, 5 Meraj
Hussein,2 George Iskander,1 Hyunseong Linus
Kim,1, 2 Boris Korzh,4 Andrew Mueller,1 Mandy Rominsky,3 Matthew
Shaw,4 Dawn Tang,1, 2 Emma E.
Wollman,4 Christoph Simon,6 Panagiotis Spentzouris,3 Neil
Sinclair,1, 2, 7 Daniel Oblak,6 and Maria Spiropulu1, 2
1Division of Physics, Mathematics and Astronomy,California
Institute of Technology, Pasadena, CA 91125, USA
2Alliance for Quantum Technologies (AQT), California Institute
of Technology, Pasadena, CA 91125, USA3Fermi National Accelerator
Laboratory, Batavia, IL 60510, USA
4Jet Propulsion Laboratory, California Institute of Technology,
Pasadena, CA 91109, USA5AT&T Foundry, Palo Alto, CA 94301,
USA
6Institute for Quantum Science and Technology, and Department of
Physics & Astronomy,University of Calgary, Calgary, AB T2N 1N4,
Canada
7John A. Paulson School of Engineering and Applied
Sciences,Harvard University, Cambridge, MA 02138, USA
(Dated: July 29, 2020)
Quantum teleportation is essential for many quantum information
technologies including long-distance quantum networks. Using
fiber-coupled devices, including state-of-the-art low-noise
super-conducting nanowire single photon detectors and off-the-shelf
optics, we achieve quantum teleporta-tion of time-bin qubits at the
telecommunication wavelength of 1536.5 nm. We measure
teleportationfidelities of ≥ 90% that are consistent with an
analytical model of our system, which includes realis-tic
imperfections. To demonstrate the compatibility of our setup with
deployed quantum networks,we teleport qubits over 22 km of
single-mode fiber while transmitting qubits over an additional 22km
of fiber. Our systems, which are compatible with emerging
solid-state quantum devices, providea realistic foundation for a
high-fidelity quantum internet with practical devices.
I. INTRODUCTION
Quantum teleportation [1], one of the most captivat-ing
predictions of quantum theory, has been widely in-vestigated since
its seminal demonstrations over 20 yearsago [2–4]. This is due to
its connections to fundamentalphysics [5–14], and its central role
in the realization ofquantum information technology such as quantum
com-puters and networks [15–19]. The goal of a quantumnetwork is to
distribute qubits between different loca-tions, a key task for
quantum cryptography, distributedquantum computing and sensing. A
quantum networkis expected to form part of a future quantum
internet[20–22]: a globally distributed set of quantum proces-sors,
sensors, or users there-of that are mutually con-nected over a
network capable of allocating quantum re-sources (e.g. qubits and
entangled states) between loca-tions. Many architectures for
quantum networks requirequantum teleportation, such as star-type
networks thatdistribute entanglement from a central location or
quan-tum repeaters that overcome the rate-loss trade-off ofdirect
transmission of qubits [19, 23–26].
Quantum teleportation of a qubit can be achieved byperforming a
Bell-state measurement (BSM) between thequbit and another that
forms one member of an entan-gled Bell state [1, 18, 27]. The
quality of the teleporta-tion is often characterized by the
fidelity F = 〈ψ| ρ |ψ〉of the teleported state ρ with respect to the
state |ψ〉accomplished by ideal generation and teleportation
[15].This metric is becoming increasingly important as quan-tum
networks move beyond specific applications, such as
quantum key distribution, and towards the quantum in-ternet.
Qubits encoded by the time-of-arrival of individualphotons, i.e.
time-bin qubits [28], are useful for net-works due to their
simplicity of generation, interfacingwith quantum devices, as well
as independence of dy-namic transformations of real-world fibers.
Individualtelecom-band photons (around 1.5 µm wavelength) areideal
carriers of qubits in networks due to their abilityto rapidly
travel over long distances in deployed opticalfibers [17, 29–31] or
atmospheric channels [32], amongother properties. Moreover, the
improvement and grow-ing availability of sources and detectors of
individualtelecom-band photons has accelerated progress
towardsworkable quantum networks and associated technologies,such
as quantum memories [33], transducers [34, 35], orquantum
non-destructive measurement devices [36].
Teleportation of telecom-band photonic time-binqubits has been
performed inside and outside the labora-tory with impressive
results [29–31, 37–42]. Despite this,there has been little work to
increase F beyond ∼ 90% forthese qubits, in particular using
practical devices that al-low straightforward replication and
deployment of quan-tum networks (e.g. using fiber-coupled and
commerciallyavailable devices). Moreover, it is desirable to
developteleportation systems that are forward-compatible
withemerging quantum devices for the quantum internet.
In the context of Caltech’s multi-disciplinary
multi-institutional collaborative public-private research pro-gram
on Intelligent Quantum Networks and Technologies(IN-Q-NET) founded
with AT&T as well as Fermi Na-
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tional Accelerator Laboratory and Jet Propulsion Labo-ratory in
2017, we designed, built, commissioned and de-ployed two quantum
teleportation systems: one at Fer-milab, the Fermilab Quantum
Network (FQNET), andone at Caltech’s Lauritsen Laboratory for High
EnergyPhysics, the Caltech Quantum Network (CQNET). TheCQNET system
serves as an R&D, prototyping, andcommissioning system, while
FQNET serves as an ex-pandable system, for scaling up to long
distances and isused in multiple projects funded currently by DOE’s
Of-fice of High Energy Physics (HEP) and Advanced Scien-tific
Research Computing (ASCR). Material and deviceslevel R&D in
both systems is facilitated and funded bythe Office of Basic Energy
Sciences (BES). Both systemsare accessible to quantum researchers
for R&D purposesas well as testing and integration of various
novel de-vices, such as for example on-chip integrated
nanopho-tonic devices and quantum memories, needed to up-grade such
systems towards a realistic quantum inter-net.Importantly both
systems are also used for improve-ments of the entanglement quality
and distribution withemphasis on implementation of protocols with
complexentangled states towards advanced and complex quan-tum
communications channels. These will assist in stud-ies of systems
that implement new teleportation proto-cols whose gravitational
duals correspond to wormholes[43], error correlation properties of
wormhole teleporta-tion, on-chip codes as well as possible
implementation ofprotocols on quantum optics communication
platforms.Hence the systems serve both fundamental quantum
in-formation science as well as quantum technologies.
Here we perform quantum teleportation of time-binqubits at a
wavelength of 1536.5 nm with an averageF ≥ 90%. This is
accomplished using a compact setupof fiber-coupled devices,
including low-dark-count sin-gle photon detectors and off-the-shelf
optics, allowingstraight-forward reproduction for multi-node
networks.To illustrate network compatibility, teleportation is
per-formed with up to 44 km of single-mode fiber betweenthe qubit
generation and the measurement of the tele-ported qubit, and is
facilitated using semi-autonomouscontrol, monitoring, and
synchronization systems, withresults collected using scalable
acquisition hardware. Oursystems, which operates at a clock rate of
90 MHz, canbe run remotely for several days without interruption
andyield teleportation rates of a few Hz using the full lengthof
fiber. Our qubits are also compatible with erbium-doped crystals,
e.g. Er:Y2SiO5, that are used to developquantum network devices
like memories and transduc-ers [44–46]. Finally, we develop an
analytical model ofour system, which includes experimental
imperfections,predicting that the fidelity can be improved further
to-wards unity by well-understood methods (such as im-provement in
photon indistinguishability). Our demon-strations provide a step
towards a workable quantum net-work with practical and replicable
nodes, such as theambitious U.S. Department of Energy quantum
researchnetwork envisioned to link the U.S. National Laborato-
ries.In the following we describe the components of our sys-
tems as well as characterization measurements that sup-port our
teleportation results, including the fidelity of ourentangled Bell
state and Hong-Ou-Mandel (HOM) inter-ference [47] that underpins
the success of the BSM. Wethen present our teleportation results
using both quan-tum state tomography (QST) [48] and projection
mea-surements based on a decoy state method [49], followedby a
discussion of our model. We conclude by consid-ering improvements
towards near-unit fidelity and GHzlevel teleportation rates.
II. SETUP
Our fiber-based experimental system is summarizedin the diagram
of Fig. 1. It allow us to demonstratea quantum teleportation
protocol in which a photonicqubit (provided by Alice) is interfered
with one memberof an entangled photon-pair (from Bob) and
projected(by Charlie) onto a Bell-state whereby the state of
Al-ice’s qubit can be transferred to the remaining memberof Bob’s
entangled photon pair. Up to 22 (11) km ofsingle mode fiber is
introduced between Alice and Char-lie (Bob and Charlie), as well as
up to another 11 kmat Bob, depending on the experiment (see Sec.
III). Allqubits are generated at the clock rate, with all of
theirmeasurements collected using a data acquisition (DAQ)system.
Each of the Alice, Bob, Charlie subsystems arefurther detailed in
the following subsections, with theDAQ subsystem described in
Appendix A 1.
A. Alice: single-qubit generation
To generate the time-bin qubit that Alice will teleportto Bob,
light from a fiber-coupled 1536.5 nm continuouswave (CW) laser is
input into a lithium niobate intensitymodulator (IM). We drive the
IM with one pulse, or twopulses separated by 2 ns. Each pulse is of
∼65 ps fullwidth at half maximum (FWHM) duration. The pulsesare
produced by an arbitrary waveform generator (AWG)and amplified by a
27 dB-gain high-bandwidth amplifierto generate optical pulses that
have an extinction ratioof up to 22 dB. We note that this method of
creatingtime-bin qubits offers us flexibility not only in terms
ofchoosing a suitable time-bin separation, but also for
syn-chronizing qubits originating from different nodes in anetwork.
A 90/10 polarization-maintaining fiber beamsplitter combined with a
power monitor (PWM) is usedto apply feedback to the DC-bias port of
the IM so asto maintain a constant 22 dB extinction ratio [50].
Inorder to successfully execute the quantum teleportationprotocol,
photons from Alice and Bob must be indistin-guishable in all
degrees of freedom (see Sec. III B). Hence,the optical pulses at
the output of the IM are band-passfiltered using a 2 GHz-bandwidth
(FWHM) fiber Bragg
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3
Charlie
DAQ
IM
Alice
CIR
VOA
POC
AMP
Bob
PWM
BS90|10
1
TDC
Data Analysisand StorageClock
FBG
FIS
234
LAS
FIS CIR
CIRSPDC
SHG
φMZI
EDFAIM
PWM
AMP
Cry
osta
t
PBS50|50
BPF
FBG1536 nm
signal
idler
POC
POC
FIS
AWG
ClockBS
90|10
PWM = Powermeter
PBS = PolarizingBeam Splitter
Controller POC = Polarization
φ MZI = Mach-ZehnderInterferometer
LAS = Laser
IM = Intensity Modulator
HPF = High Pass Filter
EDFA = Erbium DopedFiber Amplifier
FIS = Fiber Spool
3
4
BS1090|
SPDC = SpontaneousParametric Down Conversion
SNSPD = SuperconductingNanowire Single Photon Detector
VOA = Variable OpticalAttenuator
SHG = Second HarmonicGeneration
TDC = Time-To-DigitalConverter
FBG1536 nm
1510 nm
1510 nm
768 nm
1536 nm
1536 nm
AMP = Amplifier
AWG = ArbitraryWaveform Generator
BS = Beam Splitter
CIR = Circulator
FBG = Fiber Bragg Grating
BPF = Band Pass FilterBandwidth: 20 nm
Cryostat
BS50|50PBS PBS
1 2 HPF
HPFHPF1510 nmHPF
1510 nm
FIG. 1. Schematic diagram of the quantum teleportation system
consisting of Alice, Bob, Charlie, and the data acquisition(DAQ)
subsystems. See the main text for descriptions of each subsystem.
One cryostat is used to house all SNSPDs, it isdrawn as two for
ease of explanation. Detection signals generated by each of the
SNSPDs are labelled 1-4 and collected atthe TDC, with 3 and 4 being
time-multiplexed. All individual components are labeled in the
legend, with single-mode opticalfibers (electronic cables) in grey
(green), and with uni- and bi-chromatic (i.e. unfiltered) optical
pulses indicated.
grating (FBG) centered at 1536.5 nm to match the spec-trum of
the photons from the entangled pair-source (de-scribed in Sec. II
B). Furthermore, the polarization ofAlice’s photons is determined
by a manual polarizationcontroller (POC) in conjunction with a
polarizing beamsplitter (PBS) at Charlie. Finally, the optical
pulses fromAlice are attenuated to the single photon level by a
vari-able optical attenuator (VOA), to approximate photonic
time-bin qubits of the form |A〉 = γ |e〉A +√
1− γ2 |l〉A,where the late state |l〉A arrives 2 ns after the
early state|e〉A, γ is real and set to be either 1, 0, or 1/
√2 to
generate |e〉A, |l〉A, or |+〉A = (|e〉A + |l〉A)/√
2, respec-tively, depending on the experiment. The complex
rel-ative phase is absorbed into the definition of |l〉A.
Theduration of each time bin is 800 ps.
B. Bob: entangled qubit generation andteleported-qubit
measurement
Similar to Alice, one (two) optical pulse(s) with aFWHM of ∼ 65
ps is (and separated by 2 ns are) cre-ated using a 1536.5 nm CW
laser in conjunction with alithium niobate IM driven by an AWG,
while the 90/10beam splitter and PWM are used to maintain an
extinc-tion ratio of at least 20 dB. An Erbium-Doped FiberAmplifier
(EDFA) is used after the IM to boost the pulsepower and thus
maintain a high output rate of photonpairs.
The output of the EDFA is sent to a Type-0 period-ically poled
lithium niobate (PPLN) waveguide for sec-ond harmonic generation
(SHG), upconverting the pulsesto 768.25 nm. The residual light at
1536.5 nm is re-moved by a 768 nm band-pass filter with an
extinctionratio ≥ 80 dB. These pulses undergo spontaneous para-
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4
metric down-conversion (SPDC) using a Type-II PPLNwaveguide
coupled to a polarization-maintaining fiber(PMF), approximately
producing either a photon pair|pair〉B = |ee〉B , or the time-bin
entangled state |φ+〉B =(|ee〉B + |ll〉B)/
√2, if one or two pulses, respectively, are
used to drive the IM.
The ordering of the states refers to so-called signal andidler
modes of the pair of which the former has parallel,and the latter
orthogonal, polarization with respect tothe axis of the PMF. As
before, the relative phase isabsorbed into the definition of |ll〉B
. Each photon is sep-arated into different fibers using a PBS and
spectrallyfiltered with FBGs akin to that at Alice. Note the
band-width of the FBG is chosen as a trade-off between spec-tral
purity and generation rate of Bob’s photons [51].
The photon in the idler mode is sent to Charlie forteleportation
or HOM measurements (see Sec. III B), orto the MZI (see below) for
characterizations of the en-tangled state (see Sec. III A), with
its polarization de-termined using a POC.The photon in the signal
modeis sent to a Mach Zehnder interferometer (MZI) by wayof a POC
(and an additional 11 km of single-mode fiberfor some
measurements), and is detected by supercon-ducting nanowire single
photon detectors (SNSPDs) [52]after high-pass filtering (HPF) to
reject any remaining768.25 nm light. The MZI and detectors are used
forprojection measurements of the teleported state,
charac-terization of the time-bin entangled state, or measuringHOM
interference at Charlie. The time-of-arrival of thephotons is
recorded by the DAQ subsystem using a time-to-digital converter
(TDC) referenced to the clock signalfrom the AWG.
All SNSPDs are installed in a compact sorption fridgecryostat
[53], which operates at a temperature of 0.8 Kfor typically 24 h
before a required 2 h downtime. OurSNSPDs are developed at the Jet
Propulsion Laboratoryand have detection efficiencies between 76 and
85%, withlow dark count rates of 2-3 Hz. The FWHM
temporalresolution of all detectors is between 60 and 90 ps
whiletheir recovery time is ∼50 ns. A detailed descriptionof the
SNSPDs and associated setup is provided in Ap-pendix A 2.
The MZI has a path length difference of 2 ns and isused to
perform projection measurements of |e〉B , |l〉B ,and (|e〉B + eiϕ
|l〉B)/
√2, by detecting photons at three
distinct arrival times in one of the outputs, and varyingthe
relative phase ϕ [28]. Detection at the other out-put yields the
same measurements except with a relativephase of ϕ + π. Using a
custom temperature-feedbacksystem, we slowly vary ϕ for up to 15
hour time intervalsto collect all measurements, which is within the
cryostathold time. Further details of the MZI setup is describedin
Appendix A 3.
C. Charlie: Bell-state measurement
Charlie consists of a 50/50 polarization-maintainingfiber beam
splitter (BS), with relevant photons from theAlice and Bob
subsystems directed to each of its inputsvia a PBSs and optical
fiber. The photons are detectedat each output with an SNSPD after
HPFs, with theirarrival times recorded using the DAQ as was done
atBob. Teleportation is facilitated by measurement of the|Ψ−〉AB =
(|el〉AB − |le〉AB)/
√2 Bell state, which cor-
responds to the detection of a photon in |e〉 at one de-tector
followed by the detection of a photon in |l〉 at theother detector
after Alice and Bob’s (indistinguishable)qubits arrive at the BS
[54]. Projection on the |Ψ−〉ABstate corresponds to teleportation of
|A〉 up to a knownlocal unitary transformation, i.e. our system
produces−iσy |A〉, with σy being the Pauli y-matrix.
III. EXPERIMENTAL RESULTS
Prior to performing quantum teleportation, we mea-sure some key
parameters of our system that underpinthe teleportation fidelity.
Specifically, we determine thefidelity of the entangled state
produced by Bob by mea-suring the entanglement visibility Vent
[55], and also de-termine to what extent Alice and Bob’s photons
are in-distinguishable at Charlie’s BS using the HOM effect
[47].
A. Entanglement visibility
The state |pair〉B (and hence the entangled state|φ+〉B) described
in Sec. II B is idealized. In real-ity, the state produced by Bob
is better approximatedby a two-mode squeezed vacuum state |TMSV〉B
=√
1− p∑∞n=0
√pn |nn〉B after the FBG filter and neglect-
ing loss [56]. Here, n is the number of photons per tem-poral
mode (or qubit), p is the emission probability ofa single pair per
mode (or qubit), with state orderingreferring to signal and idler
modes. However, |TMSV〉Bapproximates a photon pair for p
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5
The results shown in Fig. 2 are fit proportional to1+Vent sin
(ωT + Φ), where Vent = (Rx−Rn)/(Rx+Rn),with Rx(n) denoting the
maximum (minimum) rate ofcoincidence events [55], ω and Φ are
unconstrained con-stants, and T is the temperature of the MZI,
findingVent = 96.4± 0.3%.
The deviation from unit visibility is mainly due to non-zero
multi photon emissions [57], which is supported byan analytical
model that includes experimental imperfec-tions [58]. Nonetheless,
this visibility is far beyond the1/3 required for non-separability
of a Werner state [59]
and the locality bound of 1/√
2 [55, 60]. Furthermore, itpredicts a fidelity Fent =
(3Vent+1)/4 = 97.3± .2% withrespect to |φ+〉 [59], and hence is
sufficient for quantumteleportation.
24.4 24.5 24.6 24.7 24.8 24.9Interferometer Temperature (°C)
0
10000
20000
30000
40000
50000
60000
Coin
ciden
ces /
(30
min
)
CQNET/FQNET Preliminary 2020
Vent: 96.4 ± 0.3%
FIG. 2. Entanglement visibility. The temperature of the
in-terferometer is varied to reveal the expected sinusoidal
vari-ations in the rate of coincidence events. A fit reveals
theentanglement visibility Vent = 96.4± 0.3%, see main text
fordetails. Uncertainties here and in all measurements are
cal-culated assuming Poisson statistics.
B. HOM interference visibility
The BSM relies on quantum interference of photonsfrom Alice and
Bob. This is ensured by the BS at Charlie,precise control of the
arrival time of photons with IMs,identical FBG filters, and POCs
(with PBSs) to providethe required indistinguishabiliy. The degree
of interfer-ence is quantified by way of the HOM interference
visibil-ity VHOM = (Rd−Ri)/Rd, with Rd(i) denoting the rate
ofcoincident detections of photons after the BS when thephotons are
rendered as distinguishable (indistinguish-able) as possible [47].
Completely indistinguishable sin-gle photons from Alice and Bob may
yield VHOM = 1.However in our system, Alice’s qubit is
approximated
from a coherent state |α〉A = e−|α|2/2
∑∞n=0
αn√n!|n〉A
with α
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600 400 200 0 200 400 600tAB (ps)
50
100
150
200
250
300
Thre
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oinc
iden
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(10
min
) a)CQNET/FQNET Preliminary 2020
VHOM: 70.9 ± 1.9%
600 400 200 0 200 400 600tAB (ps)
10
20
30
40
50
Thre
e-fo
ld c
oinc
iden
ces /
(10
min
) b) VHOM: 63.4 ± 5.9%
FIG. 3. Hong-Ou-Mandel (HOM) interference. A relative
dif-ference in arrival time is introduced between photons from
Al-ice and Bob at Charlie’s BS. HOM interference produces a
re-duction of the three-fold coincidence detection rate of
photonsas measured with SNSPDs after Charlie’s BS and at Bob. Afit
reveals a) VHOM = 70.9±1.9% and b) VHOM = 63.4±5.9%when lengths of
fiber are added, see main text for details.
BSM (see Sec. II C). Since measurement of |+〉 in oursetup by
symmetry is equivalent to any state of theform (|e〉 + eiϕ |l〉)/
√2 (and in particular the remaining
three basis states (|e〉 − |l〉)/√
2 and (|e〉 ± i |l〉)/√
2), wemay determine the average teleportation fidelity Favg =(Fe
+ Fl + 4F+)/6 of any time-bin qubit.
First, we prepare |e〉A and |l〉A with µA = 3.53×10−2,with Bob’s
idler bypassing the MZI to be detected bya single SNSPD. We measure
Fe = 95 ± 1% and Fl =96 ± 1%, conditioned on a successful
measurement of|Ψ−〉AB at Charlie, with fidelity limited by
multipho-ton events in Alice and Bob’s qubits and dark countsof the
SNSPDs [58]. We then repeat the measurementwith µA = 9.5× 10−3
after inserting the aforementioned44 km length of fiber as before
to emulate Alice, Charlieand parts of Bob being separated by long
distances. Thisgives Fe = 98 ± 1% and Fl = 98 ± 2%, with no
reduc-
tion from the additional fiber loss owing to our low
noiseSNSPDs.
Next, we prepare |+〉A with µA = 9.38 × 10−3, in-sert the MZI
and, conditioned on the BSM, we measureF+ = (1 + V+)/2 = 84.9 ±
0.5% by varying ϕ. Here,V+ = 69.7 ± 0.9% is the average visibility
obtained byfits to the resultant interference measured at each
out-put of the MZI, as shown in Fig. 4a. The reduction infidelity
from unity is due to multiphoton events and dis-tinguishability,
consistent with that inferred from HOMinterference, as supported by
further measurements andanalytical modelling in Sec. IV.
The measurement is repeated with the additional longfiber,
giving V+ = 58.6±5.7% and F+ = 79.3±2.9% withresults and
corresponding fit shown in Fig. 4b. The re-duced fidelity is likely
due to aforementioned polarizationvariations over the long fibers,
consistent with the reduc-tion in HOM interference visibility, and
exacerbated hereowing to the less than ideal visibility of the MZI
over longmeasurement times (see Sec. A 3).
The results yield Favg = 89 ± 1% (86 ± 3%) without(with) the
additional fiber, which is significantly abovethe classical bound
of 2/3, implying strong evidence ofquantum teleportation [62], and
limited from unity bymultiphotons events, distinguishability, and
polarizationvariations, as mentioned [58].
To glean more information about our teleportation sys-tem beyond
the fidelity, we reconstruct the density matri-ces of the
teleported states using a maximum-likelihoodQST [48] described in
Appendix C. The results of theQST with and without the additional
fiber lengths aresummarized in Figs. 8 and 9, respectively. As can
beseen, the diagonal elements for |+〉 are very close to theexpected
value indicating the preservation of probabili-ties for the basis
states of |e〉 and |l〉 after teleportation,while the deviation of
the off-diagonal elements indicatethe deterioration of coherence
between the basis states.The decoherence is attributed to
multiphoton emissionsfrom our entangled pair source and
distinguishability,consistent with the aforementioned teleportation
fideli-ties of |+〉A, and further discussed in Sec. IV. Finally,we
do also extract the teleportation fidelity from thesedensity
matrices, finding the results shown in Fig. 5,and Favg = 89 ± 1%
(88 ± 3%) without (with) the fiberspools, which are consistent with
previous measurementsgiven the similar µA used for QST.
We point out that the 2/3 classical bound may only beapplied if
Alice prepares her qubits using genuine singlephotons, i.e. |n =
1〉, rather than using |α
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24.2 24.4 24.6 24.8 25.0Interferometer Temperature (°C)
0
100
200
300
400Th
ree-
fold
coi
ncid
ence
s / (1
2 m
in) CQNET/FQNET Preliminary 2020
a) V+, 1: 69.9 ± 1.2%
0
100
200
300
400V+, 2: 69.5 ± 1.2%
24.0 24.2 24.4 24.6 24.8Interferometer Temperature (°C)
0
5
10
15
20
25
Thre
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oinc
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(40
min
)
b) V+, 1: 63.2 ± 9.6%
0
5
10
15
20
25
30
35
40V+, 2: 54.1 ± 6.3%
FIG. 4. Quantum teleportation of |+〉. Teleportation is
per-formed b) with and a) without an additional 44 km of
single-mode fiber inserted into the system. The temperature of
theinteferometer is varied to yield a sinusoidal variation of
thethree-fold coincidence rate at each output of the MZI (blueand
red points). A fit of the visibilities (see Sec. III A) mea-sured
at each output (V+,1, V+,2) of the MZI gives an averagevisibility
V+ = (V+,1 +V+,2)/2 of a) 69.7±0.91% without theadditional fiber
and b) 58.6± 5.7% with the additional fiber.
state method [49] and follow the approach of Refs.[29, 64].
Decoy states, which are traditionally usedin quantum key
distribution to defend against photon-number splitting attacks, are
qubits encoded into co-herent states |α〉 with varying mean photon
numberµA = |α|2. Measuring fidelities of the teleported qubitsfor
different µA, the decoy-state method allows us to cal-culate a
lower bound F dA on the teleportation fidelity ifAlice had encoded
her qubits using |n = 1〉.
We prepare decoy states |e〉A, |l〉A, and |+〉A with vary-ing µA,
as listed in Table I, and perform quantum telepor-tation both with
and without the added fiber, with tele-portation fidelities shown
in Table I. From these resultswe calculate F dA as shown in Fig. 5,
with F
davg ≥ 93± 4%
(F davg ≥ 89± 2%) without (with) the added fiber,
whichsignificantly violate the classical bound and the boundof 5/6
given by an optimal symmetric universal cloner[65, 66], clearly
demonstrating the capability of our sys-
|e |l | + Average0.0
0.2
0.4
0.6
0.8
1.0
1.2
Fide
lity
99.2
±0.6
%
97.9
±1.3
%
90.3
±5.9
%
93.0
±3.9
%
95.2
±1.2
%
95.9
±1.3
%
85.0
±1.6
%
88.5
±1.1
%
a)CQNET/FQNET Preliminary 2020
Single-photon fidelity from DSMFidelity from QST
|e |l | + Average0.0
0.2
0.4
0.6
0.8
1.0
1.2
Fide
lity
98.6
±0.9
%
98.4
±0.9
%
84.5
±3.3
%
89.2
±2.2
%
98.6
±0.6
%
96.2
±1.9
%
83.1
±5.0
%
87.9
±3.3
%
b) Single-photon fidelity from DSMFidelity from QST
FIG. 5. Quantum teleportation fidelities for |e〉A, |l〉A,
and|+〉A, including the average fidelity. The dashed line
rep-resents the classical bound. Fidelities using quantum
statetomography (QST) are shown using blue bars while the min-imum
fidelities for qubits prepared using |n = 1〉, F de , F dl ,and F
d+, including the associated average fidelity F
davg, respec-
tively, using a decoy state method (DSM) is shown in grey.Panels
a) and b) depicts the results without and with addi-tional fiber,
respectively. Uncertainties are calculated usingMonte-Carlo
simulations with Poissonian statistics.
tem for high-fidelity teleportation. As depicted in Fig.5 these
fidelities nearly match the results we obtainedwithout decoy states
within statistical uncertainty. Thisis due to the suitable µA, as
well as low µB and SNSPDdark counts in our previous measurements
[58].
IV. ANALYTICAL MODEL AND SIMULATION
As our measurements have suggested, multi-photoncomponents in,
and distinguishability between, Alice andBob’s qubits reduce the
values of key metrics includ-ing HOM interference visibility and,
consequently, quan-tum teleportation fidelity. To capture these
effects inour model, we employ a Gaussian-state
characteristic-function method developed in Ref. [58], which was
en-
-
8
qubit without long fiber with long fiberµA (×10−3) F dA (%) µA
(×10−3) F dA (%)
|e〉A 3.53 95.2 ± 1 26.6 95.7 ± 1.51.24 86.7 ± 2 9.01 98.4 ±
1.1
0 52.8 ± 3.4 - -|l〉A 3.53 95.9 ± 1 32.9 98.6 ± 0.7
1.24 90.5 ± 2 9.49 98.4 ± 1.60 52.8 ± 3.4 - -
|+〉A 9.38 84.7 ± 1.1 29.7 73.6 ± 3.02.01 83.2 ± 3.6 10.6 82.21 ±
3.9
0 52.8 ± 3.4 - -
TABLE I. Teleportation fidelities with (right column) andwithout
(center column) the 44 km-length of fiber for Alice’squbit states
prepared with varying µA. Mean photon numbersand fidelities for
vacuum states with fiber are assumed to bezero and 50%,
respectively.
abled by work in Ref. [67]. This approach is well-suitedto
analyze our system because the quantum states, oper-ations, and
imperfections (including losses, dark counts,etc.) of the
experiment can be fully described usingGaussian operators, see e.g.
Ref. [68]. We now brieflyoutline the model of Ref. [58], and employ
it to estimatethe amount of indistinguishability ζ between Alice
andBob’s qubits in our measurements of HOM interferenceand quantum
teleportation.
Distinguishability in any degree-of-freedom may bemodelled by
introducing a virtual beam splitter of trans-mittance ζ into the
paths of Alice and Bob’s relevant pho-tons. As shown in Fig. 6,
indistinguishable componentsof incoming photon modes are directed
towards Charlie’sBS where they interfere, whereas distinguishable
compo-nents are mixed with vacuum at the BS and do not con-tribute
to interference. Here ζ = 1 (ζ = 0) correspondsto the case when
both incoming photons are perfectlyindistinguishable
(distinguishable). Now we may calcu-late the probability of a
three-fold coincidence detection
event P3f between D1, D2 (Charlies’ detectors), and D3
FIG. 6. Schematic depiction of distingushability between Al-ice
and Bob’s photons at Charlie’s BS. Distinguishability ismodeled by
means of a virtual beam splitter with a transmit-tance ζ.
Indistinguishable photons contribute to interferenceat the
Charlie’s BS while distinguishable photons are mixedwith vacuum,
leading to a reduction of HOM visibility andteleportation fidelity.
See main text for further details.
(detects Bob’s signal photon) for a given qubit state ρABfrom
Alice and Bob:
P3f = Tr{ρAB(I− (|0〉 〈0|)⊗3
â1,â2,â3)
⊗ (I− (|0〉 〈0|)⊗3
b̂1,b̂2,b̂3)⊗ (I− (|0〉 〈0|)ĉ)}, (1)
where the â and b̂ operators refer to modes, which origi-nate
from Alice and Bob’s virtual beam splitters and aredirected to D1
and D2, respectively, and ĉ correspondsto Bob’s idler mode, which
is directed to D3, see Fig. 6.This allows the derivation of an
expression for the HOMinterference visibility
VHOM (ζ) = [P3f (0)− P3f (ζ)]/P3f (0), (2)
consistent with that introduced in Sec. III B. SinceAlice and
Bob ideally produce ρAB = (|α〉 〈α|) ⊗(|TMSV〉 〈TMSV|), and
recognizing that all operators inP3f are Gaussian, we analytically
derive
P3f (ζ) = 1− 2exp(−µA/2[1+(1−ζ
2)ηiµB/2]1+ηiµB/2
)
1 + ηiµB/2− 1
1 + ηsµB+
exp(−µA)1 + ηiµB
− exp(−µA)1 + (1− ηs)ηiµB + ηsµB
+ 2exp(−µA/2[1+(1−ζ
2)(1−ηs)ηiµB/2+ηsµB ]1+(1−ηs)ηiµB/2+ηsµB )
1 + (1− ηs)ηiµB/2 + ηsµB, (3)
for varied ζ, where ηi and ηs are the transmission ef-ficiencies
of the signal and idler photons, including de-tector efficiencies.
We similarly calculate the impact of
distinguishability on the teleportation fidelity of |+〉:
F (ζ) = P3f (ζ, ϕmax)/[P3f (ζ, ϕmax) + P3f (ζ, ϕmin)],(4)
where ϕmax (ϕmin) is the phase of the MZI added intothe path of
the signal photon, corresponding to maximum
-
9
(minimum) three-fold detection rates.To compare the model to our
measurements, we use the
experimental mean photon numbers for the photon-pairsource ηi =
1.2 × 10−2 and ηs = 4.5 × 10−3 as deter-mined by the method
described in Appendix B. We thenmeasure the teleportation fidelity
of |+〉 and HOM inter-ference visibility (keeping the MZI in the
system to en-sure ηs remains unchanged) for different values µA.
Theresults are plotted in Fig. 7. The data is then fitted tothe
expressions VHOM (ζ) and F (ζ) derived in our modeland graphed in
Fig. 7. The fitted curves are in very goodagreement with our
experimental values and consistentlyyield a value of ζ = 90% for
both measurements types.This implies that we have only a small
amount of resid-ual distinguishability between Alice and Bob’s
photons.Potential effects leading to this distinguishability are
dis-cussed in Sec. V.
Overall, our analytic model is consistent with our ex-perimental
data [58] in the regime of µA 100 GHz) and those generated at
Al-ice by the IM (15 GHz), leading to nonidentical filteringby the
FBG. This can be improved by narrower FBGsor by using a more
broadband pump at Alice (e.g. us-ing a mode locked laser or a
higher bandwidth IM, e.g >50 GHz, which is commercially
available). Alternatively,pure photon pairs may be generated by
engineered phasematching, see e.g. Ref. [71]. Distinguishability
owing tononlinear modulation during the SHG process could alsoplay
a role [72]. The origin of distinguishability in oursystem, whether
due to imperfect filtering or other deviceimperfections (e.g. PBS
or BS) will be studied in futurework. Coupling loss can be
minimized to less than afew dB overall by improved fiber-to-chip
coupling, lower-loss components of the FBGs (e.g. the required
isolator),spliced fiber connections, and reduced losses within
ourMZI. Note that our current coupling efficiency is equiva-lent to
∼50 km of single mode fiber, suggesting that oursystem is
well-suited for quantum networks provided loss
-
10
is reduced.While the fidelities we demonstrate are sufficient
for
several applications, the current ∼Hz teleportation rateswith
the 44 km length of fiber are still low. Higher repe-tition rates
(e.g. using high-bandwidth modulators withwide-band wavelength
division multiplexed filters andlow-jitter SNSPDs [73]),
improvements to coupling anddetector efficiencies, enhanced BSM
efficiency with fast-recovery SNSPDs [74], or multiplexing in
frequency [64]will all yield substantial increases in teleportation
rate.Note that increased repetition rates permits a reductionin
time bin separation which will allow constructing theMZI on chip,
providing exceptional phase stability andhence, achievable
fidelity. Importantly, the aforemen-tioned increases in repetition
rate and efficiency are af-forded by improvements in SNSPD
technology that arecurrently being pursued with our JPL, NIST and
otheracademic partners.
Upcoming system-level improvements we plan to in-vestigate and
implement include further automation bythe implementation of
free-running temporal and polar-ization feedback schemes to render
the photons indistin-guishable at the BSM [29, 30]. Furthermore,
several elec-trical components can be miniaturized, scaled, and
mademore cost effective (e.g. field-programmable gate arrayscan
replace the AWG).We note that our setup prototypewill be easily
extended to independent lasers at differentlocations, also with
appropriate feedback mechanisms forspectral overlap [75, 76]. These
planned improvementsare compatible with the data acquisition and
control sys-tems that were built for the systems and experiments
atFQNET and CQNET presented in this work.
Overall, our high-fidelity teleportation systems achiev-ing
state-of-the-art teleporation fidelities of time-binqubits serve as
a blueprint for the construction of quan-tum network test-beds and
eventually global quantumnetworks towards the quantum internet. In
this work,we present a complete analytical model of the
telepora-tion system that includes imperfections, and compare
itwith our measurements. Our implementation, using ap-proaches from
High Energy Physics experimental systemsand real-world quantum
networking, features near fully-automated data acquisition,
monitoring, and real-timedata analysis. In this regard our Fermilab
and CaltechQuantum Networks serve as R& D laboratories and
pro-totypes towards real-world quantum networks. The highfidelities
achieved in our experiments using practical andreplicable devices
are essential when expanding a quan-tum network to many nodes, and
enable the realizationof more advanced protocols, e.g. [18, 77,
78].
ACKNOWLEDGEMENTS
R.V., N.L., L.N., C.P., N.S., M.S. and S.X. acknowl-edge partial
and S.D. full support from the Alliancefor Quantum Technologies
(AQT) Intelligent QuantumNetworks and Technologies (IN-Q-NET)
research pro-
gram. R.V., N.L., L.N., C.P., N.S., M.S. S.X. andA.M.
acknowledge partial support from the U.S. De-partment of Energy,
Office of Science, High EnergyPhysics, QuantISED program grant,
under award num-ber de-sc0019219. A.M. is supported in part by
theJPL President and Directors Research and Develop-ment Fund
(PDRDF). C.P. further acknowledges par-tial support from the
Fermilab’s Lederman Fellowshipand LDRD. D.O. and N.S. acknowledge
partial sup-port from the Natural Sciences and Research Council
ofCanada (NSERC). D.O. further acknowledges the Cana-dian
Foundation for Innovation, Alberta Innovates, andAlberta Economic
Development, Trade and TourismsMajor Innovation Fund. J.A.
acknowledges support bya NASA Space Technology Research Fellowship.
Partof the research was carried out at the Jet
PropulsionLaboratory, California Institute of Technology, under
acontract with the National Aeronautics and Space Ad-ministration
(80NM0018D0004). We thank Jason Trevor(Caltech Lauritsen Laboratory
for High Energy Physics),Nigel Lockyer and Joseph Lykken
(Fermilab), VikasAnant (PhotonSpot), Aaron Miller (Quantum Opus),
In-der Monga and his ESNET group at LBNL, the groups ofWolfgang
Tittel and Christoph Simon at the Universityof Calgary, the groups
of Nick Hutzler, Oskar Painter,Andrei Faraon, Manuel Enders and
Alireza Marandiat Caltech, Marko Loncar’s group at Harvard, Ar-tur
Apresyan and the HL-LHC USCMS-MTD Fermilabgroup; Marco Colangelo
(MIT); Tian Zhong (Chicago);AT&T’s Soren Telfer, Rishi
Pravahan, Igal Elbaz, AndreFeutch and John Donovan. We acknowledge
the enthusi-astic support of the Kavli Foundation on funding
QIS&Tworkshops and events and the Brinson Foundation sup-port
especially for students working at FQNET andCQNET. M.S. is
especially grateful to Norm Augustine(Lockheed Martin), Carl
Williams (NIST) and Joe Broz(SRI, QED-C); Hartmut Neven (Google
Venice); AmirYacoby and Misha Lukin (Harvard); Ned Allen (Lock-heed
Martin); Larry James and Ed Chow (JPL); theQCCFP wormhole
teleportation team especially DanielJafferis (Harvard) and Alex
Zlokapa (Caltech), Mark Ka-sevich (Stanford), Ronald Walsworth
(Maryland), JunYeh and Sae Woo Nam (NIST); Irfan Siddiqi
(Berkeley);Prem Kumar (Northwestern), Saikat Guha (Arizona),Paul
Kwiat (UIUC), Mark Saffman (Wisconcin), JelenaVuckovic (Stanford)
Jack Hidary (X), and the quantumnetworking teams at ORNL, ANL, and
BNL, for produc-tive discussions and interactions on quantum
networksand communications.
Appendix A: Detailed description of experimentalcomponents
1. Control systems and data acquisition
Our system is built with a vision towards future repli-cability,
with particular emphasis on systems integra-
http://arxiv.org/abs/de-sc/0019219
-
11
tion. Each of the Alice, Bob and Charlie subsystemsis equipped
with monitoring and active feedback stabi-lization systems (e.g.
for IM extinction ratio), or has ca-pability for remote control of
critical network parameters(e.g. varying the qubit generation
time). Each subsystemhas a central classical processing unit with
the followingfunctions: oversight of automated functions and
work-flows within the subsystem, data acquisition and man-agement,
and handling of input and output synchroniza-tion streams. As the
quantum information is encodedin the time domain the correct
operation of the classicalprocessing unit depends critically on the
recorded time-of-arrival of the photons at the SNSPDs. Thus
signifi-cant effort was dedicated to build a robust DAQ subsys-tem
capable of recording and processing large volumes oftime-tagged
signals from the SNSPDs and recorded byour TDCs at a high rate. The
DAQ is designed to en-able both real-time data analysis for prompt
data qualitymonitoring as well as post-processing data analysis
thatallows to achieve the best understanding of the data.
The DAQ system is built on top of the standaloneLinux library of
our commercial TDC. It records timetags whenever a signal is
detected in any channel in co-incidence with the reference 90 MHz
clock. Time tagsare streamed to a PC where they are processed in
real-time and stored to disk for future analysis. A graphicaluser
interface has been developed, capable of real-timevisualization and
monitoring of photons detected whileexecuting teleportation. It
also allows for easy control ofthe time-intervals used for each
channel and to configurerelevant coincidences between different
photon detectionevents across all TDC channels. We expect our DAQ
sub-system to serve as the foundation for future real-worldtime-bin
quantum networking experiments (see Sec. V).
2. Superconducting nanowire single photondetectors
We employ amorphous tungsten silicide SNSPDs man-ufactured in
the JPL Microdevices Laboratory for allmeasurements at the single
photon level (see Sec. II B)[52]. The entire detection system is
customized for opti-mum autonomous operation in a quantum network.
TheSNSPDs are operated at 0.8 K in a closed-cycle sorptionfridge
[53]. The detectors have nanowire widths between140 to 160 nm and
are biased at a current current of 8to 9 µA. The full-width at half
maximum (FWHM) tim-ing jitter (i.e. temporal resolution) for all
detectors isbetween 60 and 90 ps (measured using a Becker &
HicklSPC-150NXX time-tagging module). The system detec-tion
efficiencies (as measured from the fiber bulkhead ofthe cryostat)
are between 76 and 85 %. The SNSPDs fea-ture low dark count rates
between 2 and 3 Hz, achieved byshort-pass filtering of background
black-body radiationthrough coiling of optical fiber to a 3 cm
diameter withinthe 40 K cryogenic environment, and an additional
band-pass filter coating deposited on the detector fiber
pigtails
(by Andover Corporation). Biasing of the SNSPDs is fa-cilitated
by cryogenic bias-Ts with inductive shunts toprevent latching, thus
enabling uninterrupted operation.The detection signals are
amplified using Mini-CircuitsZX60-P103LN+ and ZFL-1000LN+
amplifiers at roomtemperature, achieving a total noise figure of
0.61 dBand gain of 39 dB at 1 GHz, which enables the low sys-tem
jitter. Note that FWHM jitter as low as 45 ps isachievable with the
system, by biasing the detectors atapproximately 10 µA, at the cost
of an elevated DCR onthe order of 30 cps. Using commercially
available com-ponents, the system is readily scalable to as many as
64channels per cryostat, ideal for star-type quantum net-works,
with uninterrupted 24/7 operation. The bulkiestcomponent of the
current system is an external heliumcompressor, however, compact
rack-mountable versionsare readily available [53].
3. Interferometer and phase stabilization
We use a commercial Kylia 04906-MINT MZI, whichis constructed of
free-space devices (e.g mirrors, beamspliters) with small
form-factor that fits into a hand-heldbox. Light is coupled into
and out of the MZI usingpolarization maintaining fiber with loss of
∼2.5 dB. Theinterferometer features an average visibility of 98.5%
thatwas determined by directing |+〉 with µA = 0.07 into oneof the
input ports, measuring the fringe visibility on eachof the outputs
using an SNSPD. The relative phase ϕ iscontrolled by a
voltage-driven heater that introduces asmall change in refractive
index in one arm of the MZI.However, this built-in heater did not
permit phase stabil-ity sufficient to measure high-fidelity
teleportation, withthe relative phase following the slowly-varying
ambienttemperature of the room. To mitigate this instability,we
built another casing, thermally isolating the MZI en-closure from
the laboratory environment and controlledthe temperature via a
closed-loop feedback control sys-tem based on a commercial
thermoelectric cooler and aLTC1923 PID-controller. The temperature
feedback isprovided by a 10 kΩ NTC thermistor while the set-pointis
applied with a programmable power supply. This con-trol system
permits us to measure visbilities by slowlyvarying ϕ over up to 15
hour timescales. We remarkthat no additional methods of phase
control were usedbeyond that of temperature.
Appendix B: Estimation of mean number of photonpairs and
transmission efficiencies of signal and idler
photons
Using a method described in Ref. [55], we measurethe mean number
of photon pairs produced by Bob µBas a function of laser excitation
power before the PPLNwaveguide used for SHG. To this end, we modify
thesetup of Fig. 1 and direct each of Bob’s signal and idler
-
12
photons to a SNSPD. We then measure detection eventswhile
varying the amplification of our EDFA by way ofan applied current.
We extract events when photon pairswhich originated from the same
clock cycle are measuredin coincidence, and when one photon
originating from acycle is measured in coincidence with a photons
origi-nated from a preceding or following clock cycle, in
otherwords we measure the so-called coincidence and acciden-tal
rates. The ratio of accidentals to coincidences ap-proximates
µB
-
13
0
0.25
0.5
0.75
1Re
al P
art
CQNET/FQNET Prelim. 2020Teleportation of |e
|e e| |e l| |l e| |l l|0
0.25
0.5
0.75
1
Imag
inar
y Pa
rt
0
0.25
0.5
0.75
1
Real
Par
t
CQNET/FQNET Prelim. 2020Teleportation of |l
|e e| |e l| |l e| |l l|0
0.25
0.5
0.75
1
Imag
inar
y Pa
rt
0
0.25
0.5
0.75
1
Real
Par
t
CQNET/FQNET Prelim. 2020Teleportation of | +
|e e| |e l| |l e| |l l|0
0.25
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1
Imag
inar
y Pa
rt
FIG. 8. Elements of the density matrices of teleported |e〉,|l〉,
and |+〉 states with the additional 44 km of fiber in thesystem.The
black points are generated by our teleportationsystem and the blue
bars with red dashed lines are the valuesassuming ideal
teleportation.
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Teleportation Systems Towards a Quantum InternetAbstractI
IntroductionII SetupA Alice: single-qubit generationB Bob:
entangled qubit generation and teleported-qubit measurementC
Charlie: Bell-state measurement
III Experimental ResultsA Entanglement visibilityB HOM
interference visibilityC Quantum teleportation1 Teleportation
fidelity using decoy states
IV Analytical model and simulationV Discussion and Outlook
AcknowledgementsA Detailed description of experimental components1
Control systems and data acquisition2 Superconducting nanowire
single photon detectors3 Interferometer and phase stabilization
B Estimation of mean number of photon pairs and transmission
efficiencies of signal and idler photonsC Quantum State tomography
References