A Reconfigurable Quantum Local Area Network Over Deployed Fiber
Muneer Alshowkan, Brian P. Williams, Philip G. Evans, Nageswara S. V. Rao, Emma M. Simmerman, Hsuan-Hao Lu, Navin B. Lingaraju, Andrew M. Weiner, Claire E. Marvinney, Yun-Yi Pai, Benjamin J. Lawrie, Nicholas A. Peters, Joseph M. Lukens
TThis manuscript has been co-authored by UT-Battelle, LLC, under contract DE-AC05-00OR22725 with the US Department of Energy (DOE). TheUS government retains and the publisher, by accepting the article for publication, acknowledges that the US government retains a nonexclusive,paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for US governmentpurposes. DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan(http://energy.gov/downloads/doe-public-access-plan).
A Reconfigurable Quantum Local Area NetworkOver Deployed Fiber
Muneer Alshowkan, ∗ Brian P. Williams, Philip G. Evans, Nageswara S. V. Rao, Emma M. Simmerman, Hsuan-Hao Lu, Navin B. Lingaraju, Andrew M. Weiner, Claire E.Marvinney, Yun-Yi Pai, Benjamin J. Lawrie, Nicholas A. Peters, and Joseph M. Lukens † Quantum Information Science Group, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831 Autonomous and Complex Systems Group, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831 Department of Applied Physics, Stanford University, Stanford, California 94305, USA School of Electrical and Computer Engineering and Purdue Quantum Science and Engineering Institute,Purdue University, West Lafayette, Indiana 47907, USA Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831 (Dated: March 1, 2021)Practical quantum networking architectures are crucial for scaling the connection of quantumresources. Yet quantum network testbeds have thus far underutilized the full capabilities of modernlightwave communications, such as flexible-grid bandwidth allocation. In this work, we implementflex-grid entanglement distribution in a deployed network for the first time, connecting nodes inthree distinct campus buildings time-synchronized via the Global Positioning System (GPS). Wequantify the quality of the distributed polarization entanglement via log-negativity, which offers ageneric metric of link performance in entangled bits per second. After demonstrating successfulentanglement distribution for two allocations of our eight dynamically reconfigurable channels, wedemonstrate remote state preparation—the first realization on deployed fiber—showcasing one pos-sible quantum protocol enabled by the distributed entanglement network. Our results realize anadvanced paradigm for managing entanglement resources in quantum networks of ever-increasingcomplexity and service demands.
I. INTRODUCTION
Quantum communications networks play a key role inadvancing quantum information science (QIS). Some ex-amples where quantum networks are crucial include dis-tributed computing [1], enhanced sensing [2–4], securecommunications [5, 6], blind computing [7, 8] and thehighly anticipated quantum internet [9, 10]. In the con-text of fundamental scientific discovery, quantum net-works have potential to improve the sensitivity of as-tronomical interferometry [11, 12], and networks attain-ing entanglement-enhanced clock synchronization [13–15]should impact a variety of detection techniques based ondistributed atomic clocks, including those being exploredin dark matter searches [16, 17].Practical quantum key distribution (QKD) [18, 19]—arguably the most mature quantum application—is de-signed for two-node links; in order to scale beyond twonodes for quantum digital signatures [20–22] or secretsharing [23–29], fully connected quantum network archi-tectures are desirable.Fundamentally, any architecture should support entan-glement between distant parties on-demand as a core ca-pability, ideally in an efficient and agile manner. The-oretical approaches to extend distance based on quan-tum repeaters [30] are promising; however, the current ∗ [email protected] † [email protected] technology is still in very early stages. The current im-plementations of quantum networks at the logical levelcan be classified as point-to-point, trusted-node, point-to-multipoint, and fully connected. The simple point-to-point link is found in typical QKD implementationsbetween two remote parties, traditionally known as Al-ice and Bob [18]. The trusted-node network [31–39] con-sists of multiple point-to-point links in a partial meshfashion, where optical links terminate in trusted nodesdesigned for a given Alice-Bob pair. Communications be-tween distant nodes are enabled by intermediate nodesin a hop-by-hop paradigm [31, 32], so that end-to-endsecurity requires that all intermediary nodes be trusted.In the simplest case of point-to-multipoint networks, apassive beamsplitter can be used to enable a node tocommunicate with one of any available nodes at ran-dom [40]. Alternatively, leveraging broadband frequencyand polarization hyperentangled photons [41], dedicatedentanglement can be established between any pair ofusers by assigning frequency-correlated wavelength chan-nels. Fully connected quantum networks have recentlybeen realized in this paradigm using nested dense wave-length division multiplexers (DWDMs) [42, 43]. Re-configurable quantum links can be obtained by combin-ing such DWDMs with transparent spatial switches [44–48], although the individual channel spacings and band-widths remain fixed. By permitting flexible grid defi-nitions in addition to spatial switching, a wavelength-selective switch (WSS) offers further improvements, andhas recently been leveraged in fully connected quantumnetwork designs utilizing adaptive resource provision- a r X i v : . [ qu a n t - ph ] F e b ing [49, 50].Although showing great promise, results for fully con-nected quantum entanglement networks with dense wave-length allocation have been based on either loop-backfibers [43] or a tabletop configuration [42, 49, 50] whereall detection events occur in the same physical site. Thissimplification of time synchronization and data manage-ment procedures does not reflect the ultimate networkingobjective of nonlocal spatially distributed entanglement.Practically useful quantum networks must consist of spa-tially separated nodes with independent, heterogeneousquantum resources (stationary qubits, detectors, photonsources, etc.) synchronized to a common clock. Thenetwork architecture must be compatible with other net-working topologies to enable forming larger networks. Aquantum network will also need classical network capa-bilities in the form of a control plane for managementand a parallel data plane for classical communicationsbetween the network nodes.Here, we address these needs in the first dynamic, fullyconnected quantum local area network (QLAN) for en-tanglement distribution over deployed fiber. Combin-ing both adaptive bandwidth provisioning and simul-taneous distributed remote detection with off-the-shelfcontrol systems, the three-building campus network haseight independent entanglement channels in the lowest-loss telecommunications transmission window that aredynamically and seamlessly remotely reconfigurable, thusallowing various configurations and bandwidth alloca-tions without the need to add or remove any componentsin the setup. By measuring link throughput in termsof entangled bits per second (ebits/s), we validate thequality of each logical connection and show how differentprovisioning scenarios modify these “on demand” rates.Finally, to concretely demonstrate that the network sup-ports quantum protocols, we realize remote state prepa-ration (RSP) over all links, which to our knowledge is thefirst implementation of this quantum communicationsprotocol in any deployed network. Overall, our layerednetwork design and use of flex-grid lightwave technologyfurnish a promising concept and path toward more gen-eral quantum networks, including those supporting quan-tum computers and quantum sensors, ultimately estab-lishing a framework on which a future quantum internetcan be architected. II. SETUPA. Network Architecture
The QLAN can be described in terms of functionallayers shown in Fig. 1(a) in a manner analogous tothe Transmission Control Protocol/Internet Protocol(TCP/IP) stack [51, 52]. In general, this logical struc-ture encompasses the physical medium, routing, proto-cols, and applications that describe the behavior of eachnode in the network. In this way, we seek to bring the quantum network architecture closer to practice using thelayered model. In some ways, the quantum network lay-ers may closely mirror their classical counterparts; e.g.,the point-to-point links at the link layer are quite similarto optical channels provisioned over conventional networkbackbones using add/drop DWDM devices. On the otherhand, quantum network architectures diverge from classi-cal networks in crucial ways. For example, the no-cloningtheorem prohibits making a perfect copy of an arbitraryunknown quantum state [53], thus preventing the use ofconventional detection and retransmission techniques inoptical routing. For this reason, quantum layers maynot offer the same functionalities found in their classi-cal counterparts (e.g., error detection and correction asin the TCP/IP stack link layer) [10], and may requirefundamental refinements as the technology advances.In the QLAN, the physical layer corresponds to thephysical components where the encoded photons aretransmitted, received, and manipulated over the commu-nications medium (optical fiber in this case). Every userin the network is connected to the WSS via the deployedfiber [Fig. 1(b)]; thus, the physical connections of thisnetwork correspond to the star topology option depictedin Fig. 1(c). In the link layer, the WSS partitions thereceived bandwidth and dynamically routes the corre-lated spectral slices to particular output ports. In termsof entanglement distribution, the transport layer can beviewed as a logical fully connected mesh topology; eachlink forms a private point-to-point connection betweentwo nodes as in the “Full Mesh” option in Fig. 1(c). Be-cause of the nonlocal nature of quantum entanglement,private logical connections appear even without a corre-sponding direct physical link: in other words, a star phys-ical topology—central source connected to all N nodes—is able to support a logical fully connected mesh, withentanglement connections between all N ( N − / (b)(d) (c)(a) WSS
N1N2 N4N3N1N2 N4N3N1N2 N4N3N1N2 N4N3 P h y s i c a l L i n k T r a n s p o r t A p p li c a t i o n CommunicatonsProtocols
WSS
Source
WSS WSS Source
N2 N3 N4N5N6N7N8N9N1
Star Full Mesh S N1 N2 N3 N4N5N6N7N8N9
FIG. 1. (a) QLAN communication layers and services. The physical layer includes the optical components where the photonstravel and are manipulated, the link layer slices the spectrum and routes each slice to a particular user, the transport layer isthe quantum-correlated network where a pair of users shares entanglement, and the application layer uses the entangled pairs toperform a service. (b) Single WSS configuration: the input spectrum is sliced and routed to the output ports. (c) Comparisonof physical (star) and logical (fully connected mesh) topologies in network design. (d) Nested WSS where a portion of thespectrum is routed from the first to the second WSS, thereby expanding the number of nodes connected by the entanglementsource. tion possible even with relatively simple quantum net-works, in turn demonstrating a promising path forwardfor managing quantum resources in a scalable fashion.
B. Source Description
Our QLAN utilizes an entangled photon source basedon a 10 mm-long, periodically poled lithium niobate(PPLN) waveguide (HC Photonics), engineered for type-II spontaneous parametric down-conversion (SPDC).Pumping the PPLN waveguide with a continuous-wavelaser ( λ = 779 . | ψ (cid:105) ∝ (cid:90) dω Φ( ω ) (cid:104) ˆ a † H ( ω )ˆ a † V (2 ω − ω )+ e iφ ˆ a † V ( ω )ˆ a † H (2 ω − ω ) (cid:105) | vac (cid:105) . (1)Here Φ( ω ) is the crystal phase-matching function withfull-width at half-maximum bandwidth of ∼ a † H ( V ) ( ω ) generates a photon at frequency ω with horizontal (vertical) polarization, and ω is halfthe pump frequency ( ω / π = 192 . φ is compensated by the method de-scribed in Sec. III A, leaving the ideal Bell state | Ψ + (cid:105) = √ ( | HV (cid:105) + | V H (cid:105) ) for every pair of energy-matched fre-quencies. Further details regarding the preparation ofthe photon source can be found in Ref. [49].This state is then sectioned into bands that are dis-tributed to network users. We utilize a WSS to define
TABLE I. DWDM ITU 25 GHz grid C-band channel numbersof the signal and the idler photons. The pair of channels inthe same row are entangled. Fidelities are with respect tothe ideal polarization Bell state | Ψ + (cid:105) , and both photons aremeasured locally at the source prior to transmission. Ch. Signal Idler FidelityITU THz ITU THz . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . n has a width of ∆ ω/ π = 25 GHz and aligns tothe International Telecommunication Union (ITU) grid(ITU-T Rec. G.694.1) as listed in Table. I, centered at ω n = ω ± ∆ ω ( n − ) for the signal (idler). These chan-nels occupy a ∼ ∼
17 mW). The channel numbersfor the 25 GHz-wide signal and idler bins correspond to
Coincidences [5 s]
Channel Number (Signal) C h a nn e l N u m b e r ( I d l e r ) FIG. 2. Joint spectral intensity of the source measuredlocally with SNSPDs and plotted as a function of the signaland idler channel numbers. Each point is obtained with a 5 nscoincidence window and 5 s integration time. the ITU mapping in Table I. Strong correlations are ob-served for energy-matched channels, with small crosstalkin the lower off-diagonal. Overall, the coincidence-to-accidental ratio (average of matched bins divided by av-erage of mismatched bins) is 11.4.To characterize the quality of polarization entangle-ment for these eight channel pairs, we measure two-photon correlations in the
H/V and
D/A bases, defin-ing | D (cid:105) = √ ( | H (cid:105) + | V (cid:105) ) and | A (cid:105) = √ ( | H (cid:105) − | V (cid:105) ). Weemploy the Bayesian tomography method of Ref. [57] forquantum state reconstruction such that, though two setsof measurements (both in H/V and
D/A bases) are nottomographically complete, we can still obtain meaning-ful state estimates with low error bars due to the highlycorrelated nature of our input state. We confirm high fi-delity with respect to | Ψ + (cid:105) for each individual biphotonchannel as shown in Table I. C. Time Synchronization
As every node in the network is spatially distributed,independent receivers are required to evaluate net-work performance and perform quantum communica-tions tasks. For accurate photon coincidence counting,all time-to-digital converters (TDCs) in the network mustbe synchronized to a common clock. Such distributedtiming synchronization presents a critical technical chal-lenge in extending tabletop quantum networking experi-ments to the field. And the timing requirements in quan-tum communications are frequently much tighter than forclassical LANs. For example, the precision time proto-col (PTP) is a simple and ubiquitous standard for syn-chronizing devices over ethernet, yet it is designed to at-tain only sub- µ s jitter [58], whereas sub-ns precision isdesired in many photon counting quantum networkingexperiments. As a major improvement on PTP, White (a) C oun t s Time Pulse Delay [ns]420 (b) C oun t s -50 500 σ = 12.1 ns σ = 14.7 ns x10 x10 σ σ FIG. 3. Histogram of relative delays between time pulses fromtwo GPS receivers. (a) Alice and Bob. (b) Charlie and Alice.
Rabbit [59] leverages synchronous ethernet to attain ps-level precision. Accordingly, White Rabbit appears par-ticularly promising for future quantum networks, but re-quires protocol-compatible ethernet infrastructure. Al-ternatively, as lower-level, fully optical approaches, quan-tum communications experiments have utilized opticalsync pulses or direct tracking of either pulsed quantumsignals [46, 60] or photon coincidence peaks [61–64] tocompensate for the drift in independent clocks.In our QLAN, we selected GPS-based synchronizationfor its simplicity, cost-effectiveness, and availability (aGPS antenna was already available in one lab). Fromthe GPS signal, both time pulses—at a rate of one pulseper second (PPS)—and a 10 MHz clock can be derived.Before deployment on our network, we characterized thejitter between time pulses produced by pairs of indepen-dent receivers (Trimble Thunderbolot E). Histograms ofthe relative delays recorded over several hours using atime interval counter (Stanford Research Systems SR620)appear in Fig. 3, for two pairs of the three devices. Thedistributions of relative delays have standard deviationsof 12.1 ns for the devices of Alice and Bob [Fig 3(a)]and 14.7 ns for Charlie and Alice [Fig. 3(b)]. This sug-gests coincidence windows up to ∼
30 ns would be rea-sonable in our network; in practice, we found a windowof 10 ns to offer a reasonable balance between countingphoton pairs and reducing the noise from accidentals.At these jitters, GPS offers significantly higher precisionthan PTP, though upgrading to a system reaching sub-nslevels would be an important improvement moving for-ward.
III. IMPLEMENTATIONA. Deployed Network
The experiment was performed in three buildings onthe Oak Ridge National Laboratory (ORNL) campus, asdepicted in Fig. 4. The source and Alice are co-locatedin the same lab while Bob and Charlie reside in sep-arate buildings, connected to the source through totalfiber path lengths of approximately 250 m and 1200 m,respectively. The source of the polarization-entangledphotons and each user in the network are connected to aWSS by a single fiber, where the outputs pass through amanual fiber-based polarization controller (FPC) to com-pensate for the polarization rotation along the fiber path.The output of the FPC goes directly to the polarizationanalyzer for Alice and to the fiber patch panel for Boband Charlie. From the patch panel, the fibers traversemultiple communication rooms before reaching the pan-els at Bob and Charlie. The fiber from the patch panel ineach location is then routed to the polarization analyzer.The output of Bob’s polarization analyzer is sent directlyto an InGaAs avalanche photodiode (APD), whereas forAlice and Charlie, the outputs are directed to SNSPDspreceded by FPCs to maximize detection efficiency.While each user could employ a local antenna, it wassimpler in our case to share the GPS signal from the an-tenna at Bob’s location with the other nodes via RF overfiber (RFoF). The RF GPS signal at Bob is connected toa commercial RFoF transmitter that outputs an opticalsignal. This is subsequently split and sent over separatestrands of the deployed fiber to every node’s RFoF re-ceiver, which then outputs the original RF GPS signal.The GPS receivers at each network node synchronize anFPGA-based TDC with the 10 MHz and 1 Hz (PPS)clocks; we bin each detection event to 5 ns resolutionusing the FPGA’s internal 200 MHz clock, tracking thenumber of 10 MHz and 1 Hz cycles to assign a global net-work timestamp. Note that our approach offers a generaland scalable framework for increasing the network size,as bringing an additional node online requires a single-photon detector and relatively inexpensive off-the-shelfelectronic components.For data transfer and instrument control between thenodes, we set up a classical network managed by a controlplane for routing over the campus networking infrastruc-ture. Events recorded by each TDC are shared over thecontrol plane for data analysis and coincidence counting.This dedicated network allows timely and accurate datatransfer for analysis and monitoring. It is crucial to havea classical network with bandwidth commensurate withthe quantum data gathered. In our experiments, eachtime stamp is a 32-bit record, and events occur at ratesup to ∼ s − at the SNSPD nodes, corresponding toan average data rate of ∼ ∼ η ≥ η ≈ µ s, and gate window33.5 ns at 15 MHz. The heterogeneous detectors resultin widely varying link efficiencies and reflect the types ofvariability in quantum resources that should be expectedin larger quantum networks.Due to random birefringence effects induced by thesingle-mode optical fiber, careful compensation of po-larization rotation must be performed in order to real-ize high-fidelity entanglement distribution. Given thefact all fibers are located either indoors or underground,we did not find it necessary to perform active polariza-tion tracking [65, 66] the polarization state was typicallystable for hours at a time. However, we did performmanual compensation before each experiment utilizingFPCs at the outputs of the WSS. Following an align-ment procedure similar to previous fiber-based polariza-tion sources [67], we first inserted a polarizer after thebiphoton source that permitted only H -polarized pho-tons to pass through, adjusting each FPC to minimizethe counts when the analyzers are set to measure the V state, i.e., fast axis of the QWP (HWP) oriented at0 ◦ (45 ◦ ) with respect to horizontal. This ensures com-pensation of H/V individually, up to an unknown phasebetween H and V .This residual phase amounts to an output state ofthe form | HV (cid:105) + e iφ | V H (cid:105) , which we can compensate bydefining effective
D/A axes. That is, setting the fast axisof the QWP for both receivers to 45 ◦ with respect to hori-zontal, we tune the HWP angle on one of the two photonsto maximize coincidences and define the D/D measure-ment for both receivers: all other basis state projectionsare obtained by rotating the HWP by fixed amounts rel-ative to each D setting. This correction can be under-stood intuitively on the Poincar´e sphere as a rotationthat maintains an equal H/V superposition but changesthe relative phase between them [68]. Specifically, defin-ing QWP and HWP angle pair ( θ Q , θ H ), we have themeasurement settings H = (0 ◦ , ◦ ), V = (0 ◦ , ◦ ), D = (45 ◦ , x ◦ ), A = (45 ◦ , x ◦ + 45 ◦ ), R = (45 ◦ , x ◦ + 22 . ◦ ),and L = (45 ◦ , x ◦ − . ◦ ), where x is a free parameterchosen to maximize contrast. In the current experiment,we optimize the x of one polarization analyzer individ-ually for each pair of nodes, but it is important to notethat the number of free parameters (three) is sufficient tooptimize the HWP settings for all pairs of nodes simulta-neously , by solving a system of equations or monitoringcorrelations in complementary bases in real-time, similarto the techniques mentioned in Refs. [42, 69]. FIG. 4. Map of QLAN on ORNL campus. The receiver configurations at each node are shown as insets. APD: avalanchephotodiode. CW: continuous-wave laser. FPC: fiber polarization controller. FPGA: field-programmable gate array. GPS:Global Positioning System. HWP: half-wave plate. MC: motion controller. Panel: fiber-optic patch panel. BS: beamsplitter.PBS: polarizing beamsplitter. PPLN: periodically poled lithium niobate. PPS: pulse per second. Source: entanglement source.QWP: quarter-wave plate. RFoF Rx: RF over fiber receiver. RFoF Tx: RF over fiber transmitter. RPi: Raspberry Pimicroprocessor board (to control MCs). SNSPD: superconducting nanowire single-photon detector. WSS: wavelength-selectiveswitch.
B. Bandwidth Allocation 1
The eight-channel polarization-entangled source sup-ports a variety of bandwidth allocations that can be tai-lored to match a desired network configuration. Throughthe WSS, adjustments to bandwidth provisioning can bemade in real-time without modifying any fiber connec-tions. This approach for entanglement distribution wasrecently realized in a tabletop experiment [49], and herewe demonstrate it in a deployed fiber-optical network forthe first time.Given the imbalance in system efficiency, due to boththe deployed fiber loss and heterogeneous detector tech-nology, we explore and test two different bandwidth allo-cations. A patch-panel to patch-panel link loss of 1.8 dB(3.3 dB) was measured from Alice to Bob (Charlie); com-bined with the detectors used, Charlie and Alice enjoythe highest overall efficiency, followed by Alice and Boband finally Bob and Charlie. In the first allocation, weseek to balance the entanglement rates by assigning thespectral slice with lowest flux (Ch. 8) to Charlie and Al-ice (C–A), the brightest slice (Ch. 1) to Alice and Bob(A–B), and the remaining (Ch. 2–7) to Bob and Charlie(B–C).At a pump power of 15.6 mW, the average singlescounts in this allocation for each pair (in units of s − ) are:1 . × and 5 . × (A–B), 7 . × and 1 . × (B–C), and 1 . × and 4 . × (C–A). To measure statequality, we perform polarization tomography on data ob-tained with a 10 ns coincidence window and 60 s inte- gration time. Figure 5(a) shows the Bayesian mean esti-mated [57] density matrices for each pair of nodes, againbased on measurements in the H/V and
D/A bases. Inthese tests, only the logical link under test is bright (theother channels are blocked) to reduce the background ateach detector; this is equivalent to spectrally resolveddetection at each node. Nevertheless, no accidentals aresubtracted from these results, and the fidelities with re-spect to | Ψ + (cid:105) follow in Table II.From fidelities alone, it is not immediately clear howuseful the provided entanglement in the network is forgeneric quantum communications tasks. Since we haveperformed full state tomography, this could in prin-ciple be predicted for any desired protocol. But forgreater generality, we propose an “entanglement band-width” analogous to bit rates in classical links. Distillableentanglement—the asymptotic rate of pure Bell pairswhich could be produced from copies of the state, localoperations, and classical communications [70]—seems es-pecially fitting as such a quantifier, but it is extremelydifficult to compute, even with full knowledge of thedensity matrix. As an alternative, we consider the log-negativity E N [71], which provides an upper bound ondistillable entanglement. (For two qubits specifically, E N > E N thus gives a generic metric for link per-formance in terms of entangled bits (ebits) per second( R E ). Computing E N and R E from the Bayesian sam-ples, we obtain the results in the final two columns of TABLE II. Link data for both bandwidth allocations.
Alloc. Link Ch. Fidelity E N [ebits] R E [ebits/s] . ± .
03 0 . ± .
08 56 ± . ± .
06 0 . ± . ± . ± .
01 0 . ± .
03 206 ±
62 A–B 3 0 . ± .
03 0 . ± .
09 57 ± . ± .
04 0 . ± . ± . ± .
02 0 . ± .
05 320 ± Table II. Importantly, even the lowest-fidelity link (B–C) possesses an R E greater than zero by approximatelythree standard deviations. C. Bandwidth Allocation 2
In the second allocation, our goal was to improve thelowest fidelity in the network and test the performanceof different allocations for the other links. In general, atradeoff exists when selecting channel allocations: assign-ing more channels to a pair of users increases the numberof entangled photons, boosting the coincidence rate, yetit can also result in lower fidelity due to increased acci-dentals (which scale quadratically with flux) and highersensitivity to wavelength-dependent birefringence (fromthe broader bandwidth). How these effects play out inthe overall entanglement rate R E is difficult to predict.So to explore the interplay between them, we next assignCh. 1–2 to B–C, Ch. 3 to A–B, Ch. 4 to C–A, leavingthe remaining four channels unassigned as examples of re-sources available for future use should additional nodescome online.The average singles counts in Allocation 2 (units ofs − ) are: 1 . × and 5 . × (A–B), 6 . × and6 . × (B–C), and 1 . × and 8 . × (C–A). Thedensity matrices obtained follow in Fig. 5(b), along withthe specific fidelities and entanglement rates in Table II.Compared with Allocation 1, the A–B link maintainssimilar performance in all categories. B–C experiencesan appreciable increase in fidelity but, due to the re-duced flux, a slightly lower R E . Interestingly, the higherflux on the C–A link reveals the exact opposite behavior:lower fidelity but higher R E . These examples highlightthat the optimal allocation may depend on a given objec-tive: what characteristics are most valuable to the userson a network? In light of the variety of possible answersto this question, bandwidth provisioning with the WSSoffers exceptional flexibility compared to a fixed wave-length configuration: it can adapt and meet changingdemands, apportioning resources for seamless service toeach link without physical disconnections [49]. IV. REMOTE STATE PREPARATION
As a proof-of-principle application of our QLAN, weperformed the RSP protocol between network nodes.RSP is a quantum communications protocol similar butsimpler than teleportation. Like teleportation, it requiresusers to share entanglement and classical communica-tions. However, RSP uses a single-photon measurementon half the entangled pair instead of Bell state analysis onthe to-be-teleported input photon and half the entangledpair. In RSP, the sender measures one photon of an en-tangled pair in order to prepare the remaining particle atthe receiver in some desired quantum state [73–76]. Wenote this is non-deterministic, though in some cases, theclassical communications enable one to apply a unitaryoperation to yield the desired state, or to simply post-select the successful events as we have done here. Withinthe network layer architecture of Sec. II A, RSP resides inthe application layer, leveraging the logical connectionsprovided by the transport layer—i.e., the entanglementresources as summarized in Table II. The ideal Bell state | Ψ + (cid:105) is maximally correlated in all three standard polar-ization bases (rectilinear, diagonal, and circular): | Ψ + (cid:105) ∝| HV (cid:105) + | V H (cid:105) = | DD (cid:105) − | AA (cid:105) = | RR (cid:105) − | LL (cid:105) . (We adoptthe convention | R (cid:105) ∝ | H (cid:105) + i | V (cid:105) and | L (cid:105) ∝ | H (cid:105) − i | V (cid:105) .)Thus, a simple RSP experiment follows from measuringin one of these bases and performing tomography on theremaining photon, comparing the result to the ideal case.We implement RSP of a single state on each link ofthe network, utilizing Allocation 2 above. For link A–B, Alice prepares the state | R (cid:105) at Bob by projecting herphoton onto | R (cid:105) ; for B–C, Charlie prepares the state | V (cid:105) at Bob by projecting his photon onto | H (cid:105) ; and for C–A, Alice prepares the state | D (cid:105) at Charlie by projectingher photon onto | D (cid:105) . The results of Bayesian tomogra-phy on the prepared qubits are plotted on the Poincar´esphere in Fig. 6, based on measurements in a completeset of two-dimensional mutually unbiased bases ( H/V , D/A , and
R/L ). Each cloud consists of 1024 samplesfrom the posterior distribution, giving a visual indica-tion of the uncertainty in each result [77]. Fidelities withrespect to the target state are provided for each link,including error bars from the standard deviation of theretrieved samples. As expected, the C–A link gives thehighest fidelity and lowest uncertainty, followed by A–Band B–C. The experimentally measured RSP states arein excellent agreement with predictions based on the den-sity matrices in Fig. 5(b): their fidelities with respect tothe relevant partially traced density matrix are ∼ Re ρ B Im ρ B − HHHVVH VV HH HV VHVV − HHHVVH VV HH HV VHVV − HHHVVH VV HH HV VHVV − HHHVVH VV HH HV VHVV − HHHVVH VV HH HV VHVV − HHHVVH VV HH HV VHVV Re ρ B Im ρ B − HHHVVH VV HH HV VHVV − HHHVVH VV HH HV VHVV − HHHVVH VV HH HV VHVV − HHHVVH VV HH HV VHVV − HHHVVH VV HH HV VHVV − HHHVVH VV HH HV VHVV (a) (b)
A-BB-CC-A A-BB-CC-A
FIG. 5. Density matrices estimated by polarization tomography for each pair of users for (a) Allocation 1 and (b) Allocation 2.
Alice to Charlie , | 𝐷⟩ F = Charlie to Bob , | 𝑉⟩ F = Alice to Bob , | 𝑅⟩ F = FIG. 6. Tomography results for qubit states remotely pre-pared on each logical link.
V. DISCUSSION
In this work, we have successfully demonstrated thefirst adaptive bandwidth provisioning for entanglementin a deployed network, showing how allocations impactboth fidelity and entanglement rates and enable dy-namic quality-of-service provisioning. All results abovewere presented without accidental subtraction, confirm-ing that appreciable entanglement is distributed to alluser pairs under current conditions. However, from atechnical perspective, reducing noise from accidentalswould offer major performance improvements. Table IIIdisplays the results obtained for both allocations if wedo subtract accidentals prior to tomography, where theaccidentals correspond to the coincidences in a 10 nswindow that is time-shifted from the correlated peak. The fidelities in all cases are > R E are equal within errorto the raw results in Table II. While we are unaware ofany theoretical requirement for this relationship, intu-itively it makes sense: subtracting accidentals eliminatesnoise from the data, but it does not increase the through-put of entangled pairs.)Perhaps the most effective technical direction to re-duce noise would be improving the time synchronizationacross the QLAN. With the current GPS clocks, ourcoincidence windows are 10 ns, yet the detector-jitter–limited coincidence peaks are much less than 1 ns wide.Accordingly, reducing network jitter—through an opti-cal sync or White Rabbit—and using a 1 ns coincidencewindow would reduce accidentals 10-fold while maintain-ing the number of correlated detections at the presentlevel. Under such conditions, the added noise from allchannels transmitting simultaneously would prove muchmore manageable.In general, polarization entanglement seems to be par-ticularly well-suited to QLANs, where relatively shortand environmentally protected fibers result in low po-larization mode dispersion and minimal drift with time.Indeed, with the level of stability obtained in subma-rine fibers, polarization encoding has been harnessed suc-cessfully on scales of ∼
100 km without active compen-sation [78]. By replacing the current biphoton sourcewith one covering the entire C-band (1530–1570 nm) orbeyond [47, 79, 80] and leveraging nested WSSs as inFig. 1(d), one can envision much larger networks utiliz-ing the same technology. As an example, suppose thatthe bandwidth of the source in Fig. 1(d) is divided intothree sections, each frequency-correlated. One sectionis distributed among the outputs of the first WSS andthe second section to those of the nested WSS (i.e., thefirst WSS passes this entire section to the second WSS).This enables each WSS to form a QLAN where nodes inthe same QLAN are able to form a fully connected net-work. The third section can then be routed or dividedbetween the WSSs (on-demand) to form logical links be-tween these two QLANs (internetworking). In this way abasic quantum internet, in the literal sense as “intercon-nected networks,” can be realized with small upgrades tothe present system.Finally, the question of how best to characterize thegeneric quality of a quantum network remains open. Aswe have observed here, optimizing one metric may nega-tively impact others, and so the best configuration maydepend strongly on the application. Interestingly, thisgoal of quantum network benchmarking mirrors similarobjectives in quantum computing, where the concept ofquantum volume has been proposed to account for boththe number of qubits and gate performance in a consis-tent framework [81]. So while it remains to be seen what(if any) metric will prove the most informative for eval-uating quantum networks, our exploration of an entan-glement rate in ebits/s forms an important step in thisdirection, as it is able to integrate both the quality andquantity of entanglement resources into a single value.
ACKNOWLEDGMENTS
We thank S. Hicks for assistance in setting up the con-trol plane. This work was performed in part at Oak Ridge National Laboratory, operated by UT-Battelle forthe U.S. Department of Energy under contract no. DE-AC05-00OR22725. Funding was provided by the U.S. De-partment of Energy, Office of Science, Office of AdvancedScientific Computing Research, through the Early Ca-reer Research Program and Transparent Optical Quan-tum Networks for Distributed Science Program (FieldWork Proposals ERKJ353 and ERKJ355). N.B.L. ac-knowledges funding from the Quantum Information Sci-ence and Engineering Network (QISE-NET) through theNational Science Foundation (1747426-DMR). B.J.L. and
TABLE III. Accidentals-subtracted link data for both band-width allocations.
Alloc. Link Ch. Fidelity E N [ebits] R E [ebits/s] . ± .
005 0 . ± .
01 52 . ± . . ± .
006 0 . ± .
03 33 ± . ± .
001 0 . ± .
005 207 ±
12 A–B 3 0 . ± .
004 0 . ± .
02 53 . ± . . ± .
005 0 . ± .
01 24 . ± . . ± .
001 0 . ± .
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