Quantum information processing with space-division multiplexing optical fibres
QQuantum information processing with space-division multiplexing optical fibres
Guilherme B. Xavier ∗ and Gustavo Lima
2, 3, † Institutionen f¨or Systemteknik, Link¨opings Universitet, 581 83 Link¨oping, Sweden Departamento de F´ısica, Universidad de Concepci´on, 160-C Concepci´on, Chile Millennium Institute for Research in Optics, Universidad de Concepci´on, 160-C Concepci´on, Chile (Dated: January 23, 2020)The optical fibre is an essential tool for our communication infrastructure since it is the maintransmission channel for optical communications. The latest major advance in optical fibre tech-nology is spatial division multiplexing (SDM), where new fibre designs and components establishmultiple co-existing data channels based on light propagation over distinct transverse optical modes.Simultaneously, there have been many recent developments in the field of quantum information pro-cessing (QIP), with novel protocols and devices in areas such as computing, communication andmetrology. Here, we review recent works implementing QIP protocols with SDM optical fibres, anddiscuss new possibilities for manipulating quantum systems based on this technology.
Quantum information processing (QIP) is a field that has seen tremendous growth over the many years since RichardFeynman’s seminal talk on the use of quantum computers to simulate physical systems [1]. When information bits areencoded on individual or entangled quantum states, a gain over traditional systems can be seen for some informationprocessing tasks. A famous example is the well-known Shor’s algorithm for prime number factorisation running ona quantum computer, where an impressive reduction in resources is obtained when compared to classical algorithms[2]. Another major application of QIP is in communication security, where the fact that unknown quantum statescannot be faithfully cloned [3] is exploited to detect the presence of an eavesdropper. This concept was used as thecore foundation behind quantum key distribution (QKD), a communication protocol designed to distribute randomprivate keys among remote parties [4, 5]. As the first application to showcase in practice the benefits of QIP, QKDhas experienced huge development ever since [6–8]. QKD is part of a more general family of protocols called quantumcommunications (QC), which includes other schemes such as quantum teleportation and entanglement swapping [9],aiming to be the communication backbone supporting future networks of quantum computers [10].During the last decades a number of technological features were developed by the telecommunication community inorder to support the continuous increase in demand for more transmission bandwidth over a communication channel.These developments have been motivated by several applications that have cropped up along the years, from theinternet to social networking and high-quality on-demand video streaming. Arguably the optical fibre has playeda major role in the success of the telecommunication infrastructure, mainly due to its high transparency and high-bandwidth support [11]. Technologies such as wavelength division multiplexing (WDM) [12], and the erbium dopedfibre amplifier (EDFA) [13, 14] have been major catalysts to the extremely high capacities and ultra-long transmissiondistances available today. The latest technological drive towards maintaining the bandwidth growth is called spatialdivision multiplexing (SDM), and it consists of employing the transverse spatial properties of a light beam to multiplexinformation and increase the data capacity [15]. SDM nowadays routinely allows hundreds of Tbit/s of transmissioncapacity [16], ensuring that the bandwidth demand can keep growing.In photonic QIP, different degrees-of-freedom (DOFs) of a single-photon such as polarisation, frequency and itstransverse momentum, are used for encoding quantum systems of arbitrary dimension [17, 18]. Of particular interest,for instance, is the strategy that relies on encoding a quantum system in terms of the transverse optical modesavailable, which provides versatility to define high-dimensional Hilbert spaces [19–24]. It has already been proven tobe useful for QIP with photonic integrated circuits [17, 25–28], aimed at improving the robustness and compactness ofexperimental setups. However, remarkably, propagation over optical fibres for such quantum states has been a majorchallenge due to the fact that many optical fibres are designed to support only the fundamental gaussian propagationmode. Although multi-mode fibres exist (and have been available before single-mode fibres), they support hundredsof modes, requiring complex auxiliary optoelectronic systems to reconstruct the original phase wavefront followingpropagation [29]. Fortunately, SDM optical fibres and components can be used to cover this gap. In this topicalreview we go through the different SDM technologies, and cover a number of key experiments that have recentlyshown the advantages and new possibilities that this technology offers for QIP. We also discuss the integration of QIPinto an SDM optical fibre-based network infrastructure. ∗ Electronic address: [email protected] † Electronic address: [email protected] a r X i v : . [ qu a n t - ph ] J a n Multi-core
FIBRE TYPES
Few-modeRing-coreFew-modemulti-core
REFRACTIVE INDEX PROFILE a D n Core 1 Core 2 Core 3Trenches a Core
Step-index Graded-index a Ring a Core 1 Core 2 Core 3
HYBRID INTERNET
MCF MCFQN QNIXP IXPIXPROADMFMF FMFRouter
Alice BobNode 2 Node 1
EPS a) b) c)
Air-coreTrenches D n D n D n FIG. 1: Optical fibres for SDM-based quantum information processing. a) Cross-section schematics of four key types of SDMfibres. b) Simplified transverse relative refractive index profile ∆ n as a function of radial distance a , taken along the dashedline in the corresponding cross-sections in a). The dashed red lines indicate geometry variations for specific fibre types. c)Hypothetical hybrid internet scheme where classical and quantum channels co-exist in SDM networks. The classical andquantum channels are allocated to different spatial modes in the fibres, i.e. different cores or transverse modes within thesame core. Additional wavelength filtering is also used depending on spatial mode isolation. Alice may communicate to Bobthrough two possible routes, depending on current network availability. The blue route (going through intermediate node 1),employs multi-core fibres to distribute single-photons and classical traffic to Bob. Cross-sections show the different occupiedcores along the links. As an example, two cores (painted red) are used as quantum channels. The other (salmon) route, usesfew-mode fibres to send the single-photons through a quantum-teleportation based link, using the entangled photons producedat intermediate Node 2 as a resource. Here a router based on a photonic integrated chip is used to connect the entangledsource to the two fibres, while allowing the classical information from Alice to pass through to Bob. Cross sections show theoccupied LP a and LP b transverse modes as examples. Please see the text for details. EPS: Entangled photon source; FMF:Few-mode fibre; IXP: Internet exchange point; MCF: Multi-core fibre; QN: Quantum node; ROADM: Reconfigurable opticaladd-drop multiplexer. I. SDM FIBRES AND COMPONENTS FOR OPTICAL COMMUNICATIONSA. SDM fibres
A typical telecommunication optical fibre is a cylindrical dielectric silica waveguide composed of a core and thesurrounding cladding, possessing extremely low losses ( < µ m, the attenuation of cross-coupled optical power between the cores exceeds severaltens of dBs, and thus they can be approximated as independent fibres in most applications. These fibres are referredto as weakly-coupled MCFs [31], and the main advantage is that multiple-input multiple-output (MIMO) receivers[32] are not needed for detection of the spatial channels. The price to be paid is a lower spatial channel density,since the cladding diameter cannot be much larger than approximately 200 µ m to avoid rupture due to bending[33]. Nevertheless successful results have recently been obtained for 19-core weakly-coupled MCFs [34]. In order tominimise inter-core coupling, lower refractive-index “trenches” or holes are often used around the cores (Fig. 1b), atthe once again expense of lower spatial density.Another alternative is to use a fibre with a single core, but which is capable of supporting more than one transversemode for light propagation [35]. Standard telecommunication multi-mode optical fibres (MMFs) are actually not veryuseful in this regard since they support many propagation modes requiring MIMO detection systems with extremelyhigh complexities [31]. Recently, significant progress has been achieved using fibres that only support a few linearlypolarised (LP) transverse modes of propagation (typically 3 or 6), the so-called few-mode fibres (FMFs) [36]. Themain difference with an SMF is a larger core area, and borrowing from MMF technology, parabolic refractive indexprofiles can be used to minimise mode group velocity dispersion (Fig. 1b). With only a few modes present intermodalcrosstalk is limited and thus MIMO decoding is feasible. Significant progress has been made recently, combining MCFswith FMFs technology, yielding fibres with multiple cores where each core can support a few modes (FM-MCFs, seeFig. 1a) [37]. Due to an increased spatial channel density, these fibres can greatly increase the transmission capacity[38]. Finally, owing to their multi-core nature, and due to the fact that the higher-order modes have a larger modefield diameter (MFD) than the fundamental LP mode, lower refractive index trenches are also employed to minimisecross-talk from adjacent cores [37, 38].Another strategy for spatial multiplexing of data channels has been the use of transverse optical modes carry-ing orbital angular momentum (OAM) [39]. A Laguerre-Gaussian beam carries discrete orbital orthogonal angularmomentum modes characterised by an integer l , called the topological charge. Each associated photon carries anOAM of l (cid:126) , where (cid:126) is Planck’s constant divided by 2 π [40]. Recently, OAM-encoded beams have been used forspatial multiplexing and to demonstrate the possibility of Tbit/s data rates over free-space links [41]. Following that,demonstrations of the transmission of these beams over optical fibres with high-index ring refractive index profileswere reported [42], thus expanding the toolbox of such optical modes towards fibre communications. These fibres areusually referred to as ring- or air-core fibres [43, 44], due to their characteristic high refractive-index ring profile (Fig.1b). B. Multiplexers and demultiplexers
Multiplexers and demultiplexers (also typically called fan-in and fan-out devices respectively) are employed tocombine and split different data streams into corresponding spatial channels in an SDM fibre. Here we shall only focuson passive components that can already be implemented directly integrated within the fibres or through photonic chips(i.e. without resorting to bulk optical elements). In common, they all take N independent single-mode input fibres,and map them onto a particular mode on the SDM fibre. For MCFs, mux/demuxes can be directly constructed usingintegrated waveguides written three-dimensionally onto silica chips using ultrafast laser writing [45]. The appropriatefibres are then connected to the chip. Alternatively, discrete components (based on fibre bundles or compact lensesfor example) may be used [46, 47]. For FMFs, devices called photonic lanterns are normally used [48], where the inputsingle-mode fibres are tapered together (in parallel) ending in a multi-mode fibre at the other end. If the single-modefibres have slightly different sized cores, then a mode-selective lantern can be built [49], yielding considerably bettermode excitation/separation than using identical single-mode inputs/outputs. Recently, lanterns built onto integratedphotonic chips have also been developed, allowing better integration possibilities [50]. For OAM-carrying opticalmodes, there are demultiplexers, typically called mode sorters, and they have been done mostly using bulk opticcomponents/active elements [51]. Recently, significant progress has been made towards all-fibre OAM sorters, thusmaking possible the use of compact and passive multiplexing elements for OAM carrying optical modes as well [52].Finally, fan-in/fan-out units for FM-MCF fibres can also be constructed in integrated photonics chips resorting to the3D-femtosecond laser writing technique and integrated lanterns [53].The previously mentioned SDM technologies can already be used to support a “hybrid internet”, where quantum andclassical communication systems co-exist (Fig. 1c). Here, as an example, one party (Alice) wishes to send informationencoded on single-photons to a remote party (Bob). Specifically they both have quantum nodes (QNs), which mightbe a quantum computer or a QKD terminal. The single-photons are to be transmitted using the telecommunicationfibre-optical infrastructure, where classical data streams will be simultaneously transmitted to maximise the use ofthe available infrastructure. This is represented by IXPs (internet exchange points), where several local data streamsare aggregated for transmission over a high-capacity optical link to another IXP for delivery. Two routes are possiblein this example for Alice’s single-photons to reach Bob: (i) the blue clockwise direction going through an intermediatenode with a reconfigurable add and drop multiplexer (ROADM), where one of the classical core channels is droppedto the intermediate IXP, and a new one is added towards the IXP at Bob. The rest of the traffic (both quantum andclassical) is forwarded to Bob. The counter-clockwise route (ii) is used by the QNs and it consists of a link enhancedby quantum repeaters [9] (a simplified version is shown where a single entangled photon pair is shared across thelink). Here, one of the modes (LP a ) is used by the entangled photons (blue from the entanglement source to Alice,and red to Bob), while the LP b mode is used for the classical channel from Alice to Bob for synchronisation andcommunication information required by quantum repeater protocols. Additional wavelength separation may be usedto avoid cross-mode contamination. The two links employ different SDM technologies, as the blue one is based onMCFs (with 2 cores used by the QNs, and 3 by the IXPs), while the salmon one is deployed with FMFs. This illustratesa possible case in network channel allocation, where routes are dynamically assigned depending on availability. Forthis to be feasible, the network must be transparent in terms of the employed SDM technology. II. QUANTUM INFORMATION WITH SDM FIBRESA. High-dimensional quantum key distribution over SDM fibres
Many fundamental and applied tasks in quantum information benefit when d -dimensional ( d >
2) quantum systems(qudits) are employed [54–56]. One popular realisation for high-dimensional photonic quantum information processingis path encoding [19–21, 23, 27, 56, 57]. A d -dimensional path-encoded qudit has the general form | ψ (cid:105) = (cid:80) dd =0 e φ d | d (cid:105) ,where | d (cid:105) represents the d th path and φ d is the relative phase in path d . A direct advantage gained in quantumcommunication when using qudits is increasing the transmission rate of QKD systems [58], due to the fact that wecan encode log d bits onto an d -dimensional quantum state. This is a similar approach to what has always been doneto increase the number of bits sent per symbol in classical communication systems. This technique is particularlyuseful, when it becomes too resource-intensive to simply increase the transmission rate by employing faster modulationand demodulation/detection opto-electronic devices. It then aims for a different approach, which takes advantage ofextra dimensions [59].QKD’s goal is to generate a shared secret string of bits (a key) between spatially separated parties (usually referredto as Alice and Bob) through the transmission of properly encoded single-photons [5]. Current experiments in opticalfibres can reach distances over 400 kms [60], and generate a few Mbit/s of final sifted key rate over metropolitandistances [61]. The security of QKD relies on the simple fact that an unknown quantum system cannot be faithfullycloned [3], and this is explored in the well known BB84 protocol [4]. Alice chooses randomly a quantum state to betransmitted and Bob does a random measurement on it, while recording the result. After many such rounds, Aliceand Bob perform classical reconciliation and post-processing procedures to distill a shared secret key. Many factorsaffect the key generation rate, from the channel losses, the optical quality of the setup to the physical specificationsof the detectors.BB84-based proof-of-principle high-dimensional quantum key distribution (HD-QKD) experiments was alreadyperformed many years ago relying on the linear transverse momentum (LTM) of single-photons [62]. The two employedbases consisted of imaging and Fourier optical systems (by changing the appropriate lenses). The main limitation ofthis scheme is that the states had to be manually prepared and measured by changing the lenses and moving pinholes.An important next step occurred when spatial light modulators (SLMs) were used, capable of dynamically generatingsets of parallel slits, which allowed the encoding of a high-dimensional qudit onto a single-photon propagating throughthese slits [63, 64]. This was then combined with synchronised FPGA (Field Programmable Gate Array) electronicsto perform the first automated BB84 session in higher-dimensions using attenuated optical pulses [65]. Here a QKDsession using path-encoded 16-dimensional quantum states was realised by dynamically using the SLMs to prepareand measure the states, allowing 4 bits to be sent in each round. On the other hand, there has been considerableeffort to implement HD-QKD using OAM encoding strategies through free-space [66], which was also later done witha fully automated setup [67] and even over free-space intra-city channels [68].The major challenge of transmitting quantum systems encoded onto transverse optical modes through optical fibresremained. Some efforts had been done a few years ago using a 30-cm-long photonic crystal fibre [69], which areunfortunately not practical for long-distance propagation. The parallel development of SDM fibres came to changethis paradigm, since spatial-mode-supporting fibres became widely available at a reasonable cost. Two experimentsperformed simultaneously kick-started this trend. In the first (Fig. 2a [70]) a 300-m-long four-core fibre was usedto perform a HD-QKD session using deformable mirrors as the phase modulators, yielding improvements over theprevious efforts with SLMs [65]. This result is the longest distance ever reported for the transmission of path-quditstates, showing that MCFs can be used for high-fidelity propagation over distances of practical interest. The otherexperiment also showed a successful HD-QKD session using a 4-core fibre, but with Alice and Bob’s hardware fullyimplemented on integrated silicon photonics circuits [71] (Fig. 2b). Thermal elements on the chip were employed toperform active modulation. Both experiments also carried out rigorous security analyses showing that much longerdistances could be achieved while still being capable of positive secret key rates. It was also shown that MCFs can G. CAÑAS et al.
PHYSICAL REVIEW A , 022317 (2017) Compared to conventional qubit-based QKD over a singlespatial mode, our results reflect that HD-QKD is still ina very early stage of development. Nonetheless, it is inthis context that this work becomes relevant. It proves theviability of transmitting with high-fidelity high-dimensionalBB84 QKD states encoded into the transverse momentum ofsingle-photons, and also paves the way for future research onthe use of multicore fibers for HD quantum cryptography. Aswe discuss in the concluding remarks and Appendix C, thereare new technological developments on solid-state devicescompatible with multicore fibers, which shall allow for muchfaster and longer distance HD-QKD schemes in the near future.
II. IMPLEMENTATION AND RESULTS
By far the most widely used QKD protocol is BB84,which requires a prepare-and-measure scheme [24]. The BB84QKD session consists of Alice (the transmitter) randomlyencoding bits of information onto single photons and thensending them to Bob (the receiver) over an optical fiber or afree-space link. Alice’s encoding procedure randomly choosesbetween states from two mutually unbiased bases (MUBs),and Bob independently also randomly chooses states betweenthe same two MUBs to perform a projective measurement oneach photon [2]. The four-dimensional BB84 QKD sessionrequires that Alice and Bob prepare eight states spanningtwo MUBs. These states will be denoted by | ϕ ( j ) i ⟩ , where i = , , , i th state of the j th MUB, with j = ,
2. The states of the first MUB are defined by ⟨ ϕ (1)1 | = [1 , , , , ⟨ ϕ (1)2 | = [1 , − , , − , ⟨ ϕ (1)3 | = [1 , , − , − ⟨ ϕ (1)4 | = [1 , − , − , ⟨ ϕ (2)1 | = [1 , , , − , ⟨ ϕ (2)2 | = [1 , , − , , ⟨ ϕ (2)3 | = [1 , − , , ⟨ ϕ (2)4 | = [ − , , , µ , at Alice’s output. In ourwork, the highest average photon number per pulsed adoptedwas µ = .
27. In this case, pulses containing only one photonare the vast majority of the nonnull pulses generated ( ∼ FIG. 1. (a) Experimental setup: Alice encodes the four-dimensional BB84 QKD states using a deformable mirror (DM1).The communication link consists of a 300-m-long four-core multicorefiber. Bob uses a deformable mirror (DM2) and a SPD to implementhis measurements. See main text. (b) The multicore fiber’s crosssection. (c) The deformable mirror is composed of a 6 × | ⟩ , | ⟩ , and | ⟩ have a relative phase of 0 applied, while | ⟩ has a π relative phaseshift. (d) Simulated FF distribution with the pinhole area indicated byred circle. The first case is when Bob’s projection is performed on thesame state as the one Alice sent. It displays constructive interference.The second case is with an orthogonal projection, leading to nodetection. The last case is when Alice and Bob use different MUBs.HWP (QWP): half (quarter) wave plate. PBS: polarizing beamsplitter. can be obtained as we discuss in the concluding remarks. Last,note that since the period between consecutive pulses is longerthan the coherence time of the laser ( ∼ . µ s), there is no needof active phase randomization of the pulses to avoid securityloopholes [33].The attenuated pulses are used by Alice to encode therequired high-dimensional quantum states. For this purposethey are initially coupled into a 10-m-long multicore fiber(MCF1), composed of four single-mode cores, by means of a10 × objective lens (L1) [See Figs. 1(a) and 1(b)]. The coremode field diameter is 8 . µ m and the cores are separated by d = . µ m to ensure that cross-talk effects are negligible.All cores of the fiber are equally illuminated. Thus, theprobability amplitudes for the photon transmission by eachcore are equally weighted. Contrary to standard fiber arrays,the cores of multicore fibers lie within the same cladding,ensuring that random phase-fluctuations induced by thermaland mechanical stress are strongly suppressed. Therefore,the state of the photons transmitted over the MCF1 is acoherent superposition given by | ⟩ = ! e i φ l | l ⟩ , where | l ⟩ denotes the state of the photon transmitted by the l thtransverse core mode, and φ l is the relative phase acquiredduring the propagation over the l th core. This is the fiducialstate which is then used to prepare the required ones for thefour-dimensional BB84 QKD session. This is done by imagingthe output face of MCF1 onto a deformable mirror (DM1)by means of a second 10 × objective lens (L2). The 10 × magnification factor is chosen such that the image of each only if Φ ; i Φ ; j !!" ¼ N (1)In other words in a set of MUBs { B , B , B , … , B k , B n } if wemeasure a state in B n basis, and this state was prepared in B k basis(with k ≠ j ), all the outputs are equally probable. It has beenproven that the maximum number of the MUBs in a Hilbert spaceof dimension N is N +1, where N is a integer power of a primenumber. In our analysis we consider the case of three MUBsreported in Eq. (2) for an Hilbert space of four dimension ( N =4).The main difference is related to the tolerable threshold of theQBER and the maximum achievable value of secret key rate. Amore detailed discussion follows in next paragraph. The set of thethreeMUBs,usedintheproposedHD-QKDsystem,canbede fi nedas a linear combination of: A j i ¼ ffiffiffi p ð Þ B j i ¼ ffiffiffi p ð Þ C j i ¼ ffiffiffi p ð Þ D j i ¼ ffiffiffi p ð Þ M ¼ A j i þ B j i A j i % B j i C j i þ D j i C j i % D j i M ¼ A j i þ C j i A j i % C j i B j i þ D j i B j i % D j i M ¼ A j i þ D j i A j i % D j i B j i þ C j i B j i % C j i (2) We can easily prove that the set M , M , M satis fi es themutually unbiased assumption, | 〈 M | M 〉 | =| 〈 M | M 〉 | =| 〈 M | M 〉 | =1/4. Physically, |A 〉 , |B 〉 , |C 〉 , and |D 〉 represent the quantumstates related to the four individual cores of a multi-core fi ber, asshown in the inset of Fig. 1a. By tuning the Mach – Zehnderinterferometers (MZIs), situated in the transmitter chip, Alice creates a quantum superposition between cores. In this way sheprepares one of the states in the three MUBs. A random numbergenerator is used for basis and states choice. Before the quantummeasurement, Bob randomly choose one of the three MUBstuning the corresponding MZI. In such a way, Bob createsinterference between different cores and he correctly measuresthe quantum states sent by Alice. As in the BB84 protocol, afterthe measurements, a distillation process is required. In thisprocedure Alice and Bob discard all the data related to a differentbasis choice. At this point Alice and Bob share an identicalquantum key, useful for encryption and decryption of the plaintext.Secret key rateOne of the most important parameters in a communicationsystem is the achievable rate. In particular, in a QKD system, themajor criterion is represented by the secret key rate: number ofbit/s or bit/pulse that Alice and Bob can establish as useful key.A general formula for the standard protocols can be written as: R & I AB % min I AE ; I BE ð Þ ; (3)where I AB represents the classical mutual information betweenAlice and Bob ( I XY = H ( X ) − H ( X | Y )), and the marginal entropy isde fi ned as H X ð Þ ¼ P x X p x ð Þ log p x ð Þ . The right term of Eq. (3),min( I AE and I BE ), is related to the quantum mutual informationbetween Alice and Eve or Bob and Eve. In the following analysiswe consider only the mutual information between Alice and Eve,but a more complete analysis can be done: in this way the secretkey rate value is estimated with a lower bound. Furthermore, wework under the assumption of trusted-device scenario, in whichEve cannot modify the ef fi ciency of Bobs detectors. In case ofququart QKD system the fi nal secret key rate formula must beadapted. The mutual information between Alice and Bob is: I AB ¼ log N ð Þþ F log F ð Þþ % F ð Þ log % FN % % & ; (4)where N is the dimension of the Hilbert space and F =1 − D represents the fi delity of Bob. D is de fi ned as the disturbance inthe communication link. In order to extract a bound on the fi nalsecret key rate, we should de fi ne the best strategy for Eve. In thefollowing analysis we consider two different kinds of Eve ’ sstrategy. Individual attacks (IAs), where Eve monitors the ququartsindependently from each other, and coherent attacks (CAs). CAsinstead are less conservative on Eve ’ s strategy, in fact she can Fig.1 a Schematic of theHD-QKD basedonMCFusing silicon PICforAlice andBob.The inset shows thecross-section of themulti-core fi ber,where four cores are used. b , d Shows the fabricated silicon PIC for Alice and Bob, respectively. c Presents the picture of the fabricated chipswith a 1 euro coin, indicating the compact size of the silicon PICs
Quantum key distribution based on multicore fi berY Ding et al. npj Quantum Information (2017) (cid:0)2(cid:0)(cid:0) Published in partnership with The University of New South Wales a)b) indistinguishability is by using a particular set of structuredmodesoflightcombiningOAMandSAM,theadvantagebeingthat these modes could be spatial-division multiplexed withthe fundamental mode, which could be encoded with polari-zation. In this Letter, we present a characterization of one suchvortex fiber, and show that it could be used for QKD in a two-dimensionalBB84protocolencodingquantuminformationonheralded single photons with spatially structured polarizationdistributions, in addition to encoding in polarization of thefundamental mode. This opens up the possibility to use struc-turedphotonfibernetworkstoincrease theclassicalbandwidthduring quantum secure transmission of information.ThevortexfiberusedinthisLetterisasolidcorevortexfiberwhich supports photons with ! ℏ units of OAM [17,28],where ℏ is the reduced Planck constant. The operating prin-cipleofthistypeofvortexfiberisthatitstransverseprofilecon-tains a ring of higher refractive index, which resembles theOAM mode shape and acts as a guide for OAM-encoded pho-tons.InadditontohavingtwoorthogonalOAMstates,photonscan simultaneously be either left- or right-handed circularly po-larizedwith ! ℏ unitsofSAM.Wewillwritestructuredphotonswith the notation j l i π , where π is the SAM value and l is theOAM value. We will further use the convention that π " and π " − correspond to left- and right-handed circular polar-izations, respectively. In the case of this vortex fiber, the stateswith the same handedness, fj i , j − i − g , are degenerate intime with each other, i.e., possess identical group velocitiesinthefiber,butnon-degeneratewithstatesofoppositehanded-ness j i − , j − i , and the other fundamental modes of thefiber [29]. Therefore, we take advantage of the states with thesame handedness for QKD protocols with this vortex fiber. Inparticular, for the BB84 protocol, we form two mutually un-biased bases (MUBs), i.e., no information is gained about thestates in one basis by making measurements in the other basis,using the aforementioned states, M " fj i , j − i − g , and M " f $ j i j − i − % ∕ ffiffiffi p , $ j i − j − i − % ∕ ffiffiffi p g . ThisLetter provides a proof-of-concept test that it is feasible to usestructuredphotons,asqubits,throughvortexfiberquantumchan-nels which, in principle, can be extended to higher dimensions.In our experiment (see Fig. 1), we generate heralded singlephotons via spontaneous parametric downconversion using a 5 mm long periodically poled potassium titanyl phosphate(ppKTP)crystalpumpedwitha405nmdiodelaser(200mW).Thephotonpairs(signal λ s "
775 nm andidler λ i "
850 nm )are separated via a dichroic mirror (DM), coupled to differentsingle-mode fibers (SMFs). We herald our single photons bydetecting the partner photon at an avalanche photodiode(APD)withadarkcountrateoflessthan50Hz,whichtriggersa coincidence counter. The single photon, on which we willimprintinformation,isfirstsenttoapairofdiffractiongratingsand a slit that acts as a narrow bandpass filter, not shown inFig. 1. A first diffraction grating and lens perform a Fouriertransformsothatthespectrumisgivenatthefocus.Amoveableslit with anadjustableslit width can thus be placed at the focusto precisely choose the desired wavelength and bandwidth.A wavelength of approximately ! .
75 nm is chosen forthe signal photon, since the fiber was designed to operate atthis wavelength. A second lens and diffraction grating performthe inverse transformation to recombine the frequencies, sub-sequently coupled back into SMFs. This adjustable filter is ap-proximately 10% efficient. With a 5 ns coincidence window,our heralded single-photon source has a rate of approximately4500coincidencespersecondafterthefilter.However,wenotethat this is not a fundamental constraint, rather a technicaldeficiency of our setup.In the preparation stage, Alice prepares the signal photoninto a state from either M or M using a sequence of waveplates and a patterned liquid crystal device known as a q -plate,where q " l ∕ is the topological charge of the liquid crystals.Such a device coherently couples SAM to OAM [30,31]. Togenerate structured photons with j l j " , a q " ∕ plateis utilized, which naturally produces states with the oppositehandedness; a half-wave plate is placed after the q -plate to cre-ate states with the same handedness, such as in M and M .The theoretical phase and polarization distributions of eachstate are displayed in Fig. 2(a). We note that the modes inMUB M possess uniformly circular polarization distribu-tions,whereasthesuperposition MUB M consistsofspatiallyvarying polarization distributions of only linear polarizations,i.e., structured modes of light. In order to compensate for bi-refringent coupling induced by the fiber, a set of compensationwave plates [29,32] (not shown in Fig. 1), consisting of two Fig. 1.
Sketch of the experimental setup. Non-degenerate photon pairs (signal λ s "
775 nm , idler λ i "
850 nm ) are produced by spontaneousparametric downconversion from a 5 mm long ppKTP crystal pumped by a 200 mW 405 nm pump diode laser; they are then split on a dichroicmirror(DM).Alicepreparestheheraldedsinglephotoninaparticularquantumstatewithasequenceofwaveplatesanda q " ∕ plate(QP),andthensendsittoBobthroughthevortexfiber(quantumchannel).Bobperformsaparticularmeasurementwithareversesequenceofwaveplatesand q " ∕ plate,recordingacoincidenceeventbetween theresult(D2)andtheheraldingtriggerphoton(D1).H,half-wave plate;Q,quarter-waveplate; LP, long-pass filter; PBS, polarizing beam splitter. Letter
Vol. 43, No. 17 / 1 September 2018 /
Optics Letters c)d)
FIG. 2: Key experimental demonstrations of QKD with SDM fibre. a) 300-m-long HD-QKD session using path-encodingwith a 4-core fibre. Reprinted with permission from [70]. b) HD-QKD session with path-encoded states based on integratedsilicon photonic circuits using 4-cores in a 3-m-long fibre. Reprinted with permission from [71]. c) Proof-of-principle QKDdemonstration using 2-dimensional OAM states through a 60 m vortex (ring-core) fibre. Reprinted with permission from[73], [OSA]. d) HD-QKD demonstration using hybrid OAM/polarization states through 1.2 km air-core fibre. Reprinted withpermission from [74]. be used to deliver keys in parallel choosing separate sets of cores [72]. More recently, ring-core-type fibres have alsobeen employed for remote QKD sessions using OAM encoded qudits. The first one (Fig. 2c) was actually done in a2-dimensional space over a 60 m vortex fibre with no active state preparation [73], while the second one (Fig. 2d)employed hybrid polarisation/OAM states to perform an HD-QKD session using ququarts over 1.2 km-long air-corefibre [74].
B. Entanglement distribution
The successful distribution of photonic entanglement over long optical fibres is an important operational toolboxin quantum information. Many experiments have been performed using different degrees of freedom of a single-photon over optical fibres, mainly using polarisation [75–78] and energy-time/time-bin [79–82]. For many years thedistribution of spatial entanglement (i.e., entanglement between quantum systems encoded in terms of the transverseoptical modes of light) over optical fibres has been out of reach. This has been mainly due to the fact that (i) single-mode fibres, by their very nature, do not support more than one spatial mode; and (ii) mode coupling scramblesthe multi-mode spatial state during propagation. Nevertheless, significant progress has been made recently usingboth custom-made and standard commercially available optical fibres. In common, all experiments employ fibres thatsupport only a few spatial modes, in order to minimize significant mode coupling.The first experiment to be able to propagate spatially entangled photons employed a 30-cm long hollow-core photoniccrystal fibre to transmit one of the photons of the pair, while successfully measuring a Bell inequality violation over thepair of qubits [69]. This was an important first step demonstrating the feasibility of distributing spatially entangledstates, but the use of specialty fibres hampers practical use. This was improved upon with standard polarisationmaintaining fibres that were used as FMFs (by working with single-photons at 810 nm), and then two of the threepossible linearly polarised modes in the fibre were used for each single-photon of the pair (LP and the even LP mode) [83].Nevertheless, one immediate advantage of resorting to spatial entanglement is the possibility of reaching higher-dimensional Hilbert spaces. When combined with fibre propagation, this allows the execution of more interesting a) b) noncollinear degenerate type-0 SPDC in a periodically poledlithium niobate (PPLN) crystal (poling period of 19.5 μ m,thickness of 1 mm), pumped by a continuous-wave diode laser(wavelength of 775 nm, nominal linewidth < , opticalpower of 30 mW). The SLM, a reflection-mode multipixelphase shifter (Hamamatsu X10468-02, × ,pixel pitch 20 μ m), applies a pattern with subsections whosenumber leads to the number ofpump beam spots. The positionand phase of each spot are determined by the direction andphase of the grating-like linear phase gradient pattern of eachsubsection, respectively, as shown in the inset of Fig. 1(a). Thebrightness and phase of each spot eventually determine thecomplex coefficient of the corresponding component of the fi-nal entangled state. The brightness is controlled by varying thearc angles of the pump beam slices to adjust the relative focusedbeam powers. The phase is controlled by shifting the gratingpattern to the phase gradient direction. Because all the spotsshare the optical components, the relative phases betweenthe spots are inherently stable, which is critical for maintainingcoherence and is not straightforward for multisource schemes.The maximum number of spots with this scheme can be esti-mated to be the cross-section area of the SPDC crystal dividedby the minimum beam spot area to guarantee a Rayleigh rangelonger than the crystal length.The end faces of two MCFs (Fibercore SM-4C1550, lengthof 50 cm, NA of 0.14 – – μ m, and single-mode cores at the vertices of a centered μ m × μ m square) are imaged onto the PPLN crystal tocapture the downconverted photons with a center wavelengthof 1550 nm. The four core images coincide with the pump beam spots that are aligned with the vertices of a centeredsquare of μ m × μ m at the crystal. Figure 1(b) showsthe lens configuration to ensure parallel propagation of all thebeams inside the crystal. The pump laser incidenton SLM0hasa ∕ e diameter of1.3 mm. The distance L (250 mm) is chosensuch that the centroids of the four sliced Gaussian beams fromSLM0 overlap at the back focal plane of L p considering thebeam propagation angles. Each optical path of the downcon-verted photons includes a f configuration ( L and L ) thatrelays images between the focal planes of L and L f , as shownin Fig. 1(b). In the real implementation, the distance between L and L was 130 mm larger than the design length(150 mm); therefore, the four core images propagate with aslight tilt angle (3.0 mrad) toward the optic axis inside thePPLN crystal.The length of the MCF is practically limited by decoherencebetween the core modes due to the intercore differential groupdelay (DGD). We note that the coherence of this entangledstate based on a continuous-wave-pumped SPDC can be main-tained even when the cores are different only if the two MCFsareidentical,andthe samecoresofthetwoMCFsarealignedtocoincide within the images at the crystal [11]. However, thecurrent MCF shows inhomogeneity along the fiber length,which hinders complete entanglement protection by geometricalignment or DGD compensation by core permutationthrough sequential offset splicings as in Ref. [28]. Therefore,the accumulated inhomogeneous DGD has to be kept smallerthan the coherence length of photons. Development of en-tangled photon pair sources with a narrower bandwidth canincrease the usable fiber length, possibly up to several hundreds (a)(b) Fig.1.
Schematicoftheexperimentalsetup.(a)Arrangementoftheopticalcomponentsusedtogenerateandmeasuretheentangledphotonpairsbetween two multicore fibers. (b) Imaging configuration for the pump beam and photons coupled to the fiber cores ( L !
250 mm , f !
50 mm , f !
75 mm , and f !
15 mm ). Inset: phase patterns on SLM0. SLM, spatial light modulator; L, lens; MCF, multicore fiber; Q, quarter-waveplate; H, half-wave plate; PBS, polarizing beam splitter; IF, interference filter; FC, fiber coupler; SMF, single-mode fiber.
20 Vol. 7, No. 1 / January 2019 /
Photonics Research
Research Article QWP@1550
PPKTP
PBS@775PBS@1550 DM HWP@775HWP@1550 PCWDMSLMSPDOAM fiberMDP
Bob’s
OAM Analysis Precompensation module
Alice’s
OAM AnalysisOAM entanglement resource
Figure 1. Schematic of the experimental setup. The entangled photons are generated by Type-II SPDC in PPKTP crystal. Theidler photon is directly measured at Alice’s part while the signal photon is fed to precompensation module and coupled into a1-kilometer-long OAM fiber and finally analyzed at Bob’s part. The single-photon detectors we use are InGaAs detectors. SLM:spatial light modulator, SPD: InGaAs single-photon detector, PC: polarization controller, WDM: wave division multiplexingwith 0.5 nm bandwidth, DM: dichroic mirrors, DP: dove prism, M: mirror.Figure 2. Density matrices of the OAM entanglement sourceand the closest MES. (a) and (c) represent the real and imagi-nary part of the density matrix of the source respectively. (b)and (d) represent the real and imaginary part of the closestMES’s density matrix respectively.
In our work, we experimentally determine the inter-modal dispersion (see METHOD) and devise a setupto introduce reverse dispersion to pre-compensate it be-fore entering the 1-km fiber. The precompensation mod-ule is comprised of two cascaded interferometers and alocking system. The former interferometer is an OAMsorter which serves as a parity check to convert thedifferent OAM to polarization according to their topo-logical charge ` . We redesign the traditional Mach-Zehnder OAM interferometer [57] into Sagnac interfer- ometer for a more robust phase stability. A half waveplate (HWP) is used to rotate polarization of signal pho-toninto ( | H i + | V i ) / p beforeenteringtheOAMsorter.Then OAM modes with odd topological charge ` = ± are converted to horizontal polarization and the even one ( ` = 0) to vertical. In the following unequal-arm Mach-Zehnder interferometer they are separated into differentpathssowecanmanipulatethemindividually. TheOAMmodeswith ` = ± willentertheshortarmand ` = 0 willenter the U-shaped long arm. To precompensate the in-termodal dispersion which will occur in the OAM fiber, adove prism in the U-shaped arm is mounted on a transla-tion stage for arm-length tuning. Furthermore, to stabi-lize relative phase in the entangled state, a phase-lockingsystem is applied to the latter Mach-Zehnder interferom-eter (depicted in Fig. 3). After the two cascaded interfer-ometers, we recombine the different LG modes and erasethe polarization degree of freedom by a half wave plate(HWP) and a polarizing beam spliter (PBS). This settinghas advantages of not only erasing the polarization butalso concentrating the three-dimensional entangled state,as we can vary the transmittance of ` = ± and ` = 0 so as to make the spiral spectrum of OAM entanglementstate more flatten.Subsequently, the signal photon is coupled into a 1km long home-designed OAM fiber (see supplementarymaterial for fiber details), which supports OAM modeswith ` = 0 , ± , ± . It is noteworthy that the modematching in this fiber must be done with very high pre-cision. There exists plenty of eigenmodes supported byOAM fiber. Analogous to coherent mode detection, thetransmission of OAM states relies on the axis-dependent FIG. 3: High-dimensional distribution of spatially entangled states through optical fibres. a) Bell inequality test over 4-corefibres. Reprinted with permission from [85]. b) Distribution of 3-dimensional OAM entanglement over a 1 km long few-modefibre. Reprinted with permission from [87]. high-dimensional quantum information tasks, where physical separation between parties who do not share line-of-sight is no longer a restriction. Going in this direction more recent experiments have taken direct advantage ofthe possibilities allowed by newly developed SDM hardware. In [84], 4-dimensional spatial entanglement has beendistributed over short-distances (30 cm) 4-core fibres. Entanglement was verified through quantum state tomography,and this was later expanded to a Bell inequality test [85] (Fig. 3a). Another experiment taking direct advantageof SDM fibres was [86], where a 1 km-long FMF was used to test if polarisation and time-bin entanglement can bepropagated through the different modes.Very recent progress has also shown the propagation of OAM entangled quantum states over optical fibres. One ofthe photons of a 3-dimensional OAM entangled state was successfully propagated over a 1 km step-index fibre [87],supporting up to 6 LP modes (Fig. 3b). The employed fibre required careful alignment of the input axis in order toproperly excite and later decode the OAM modes. This experiment also featured compensation of modal dispersion,which is necessary as the fibre length increases, even more so for entangled states produced by down-conversionprocesses, due to the typical low temporal coherence involved. Another experiment started with a polarisation-entangled photon pair, where one of the photons gets further encoded with a superposition of OAM modes (vectorvortex mode) to generate hybrid three-qubit entanglement [88]. The hybrid-encoded photon is transmitted througha 5 m-long air-core fibre, showing that hybrid high-dimensional entanglement can be propagated over SDM fibres.Then, another experiment demonstrated hybrid OAM/polarisation entanglement with one of the photons propagatedthrough 250 m of single-mode telecom fibre, which works as a FMF at the working wavelength in the experiment of810 nm [89]. The main drawback here is the much greater attenuation ( > III. INTEGRATION WITH CLASSICAL TELECOMMUNICATION OPTICAL NETWORKS
Compatibility with optical networks is a major driving force for the widespread deployment of quantum com-munication [90, 91]. The next logical step is to ensure compatibility of quantum communication systems with thenext-generation SDM optical networks. A first proof-of-principle experiment (over a short distance of 2 m) has shownthat spatial multiplexing of a classical and a quantum channel is possible on a few-mode fibre [92]. Then a compati-bility experiment between QKD and classical data co-existing in the same fibre using separate cores over a MCF wascarried out [93]. The centre core was reserved for the QKD channel, while the side cores were pairwise-filled with 10Gbit/s data streams from opposite directions. A 7-core fibre was employed with a relatively high core-to-core distance(47 µm ), such that inter-core crosstalk was rather low at -60 dB and -80 dB at the forward and backwards propagationdirectly. Nevertheless this crosstalk was still high enough to ensure that the quantum and classical channels couldnot share the same wavelengths on separate cores (Fig. 4a). If these limitations are taken into account, co-existencebetween quantum and classical signals in the same fibre is possible, as with single-mode fibres. A follow-up studycharacterised the difference in impact between trench-assisted and non-trench-assisted (TA- and NT- respectively)MCFs [94], while having the same core-to-core distance in both fibres (41.1 µm ). All cores were simultaneously loadedwith high speed traffic (112 Gbit/s), at different wavelengths. NT-MCFs are interesting to be studied for compatibil-ity, since they allow a higher core density due to the absence of lower refractive index trenches surrounding the cores.The results showed that compatibility is also possible, with a larger penalty imposed by the classical channels on the
3. QKD/data spatial multiplexing setup
Figure 3 shows our experimental setup. The 53-km, 7-core MCF spool forms the optical channels between two communicating parties, Alice and Bob. At each end of the fiber, all transmitters or receivers are terminated with SSMF’s. Optical coupling between SSMF’s and MCF is realized through two 1 × 7 fanouts featuring a coupling loss in the range of 1.0 – 4.6dB. We use a QKD system operating with a clock rate of 1 GHz and using the T12 decoy-state protocol [26]. The photons are detected with InGaAs avalanche photodiodes operating in Geiger mode and with self-differencing [27] electronics. While crucial for noise rejection in SSMF multiplexing [18], the temporal filtering capability offered by the detectors is less important in the present spatial multiplexing setup. Optical crosstalk from other channels (cores) is much less than in the SSMF case since space division gives >40dB isolation. The QKD system utilises a fully automatic FPGA control for stabilising the photon count rate and quantum bit error rate (QBER) through feedback control of the polarization controller, fiber phase delay and system delay. Error correction is accomplished using Cascade [28] and a number theoretic transform approach to execute efficient matrix multiplication is utilized for privacy amplification. The QKD system requires a quantum channel and auxiliary classical channels for clock synchronization and key reconciliation. We assign two cores of the MCF for these signals: the central core is to carry the weak quantum signal while one of the outer cores for the QKD auxiliary classical signals. The spare 5 outer cores are free to use for intense classical data communication signals. The quantum signal is transmitted on the DWDM grid with a wavelength of 1547.72 nm while all classical signals are transmitted at other wavelengths. This arrangement allows rejection of the intercore leakage into the quantum channel using a standard DWDM filter of 0.4 nm passband located in the quantum receiver. A pair of 10 Gb/s data channels, with 0 dBm power each launched into separate cores from opposite directions, are assigned at the wavelength of 1552.72 nm. The quantum channel has a total loss of 14.1 dB, consisting of 12.4 dB due to the MCF, 1.1 dB loss at the optical fanout and 0.6 dB at the DWDM filter.
Fig. 3. QKD over MCF experimental setup.
4. Results and discussion
We operate the QKD system over the central core of the MCF while bi-directional 10Gb/s classical signals are transmitted simultaneously through two of the six outer cores. A bit-error tester is used to monitor the data communication. It typically does not record a single error during the experiments. Figure 4 plots the secure key rate and quantum bit error rate (QBER) over a 24 hour period. These values are obtained through real-time data-processing, including error correction and privacy amplification, on a sifted block size of 1 × 10 bits. The block size is sufficiently large to achieve 85% of the asymptotic secure key rate [26]. Each data block is collected over a session time of about 36 seconds with a sifted bit rate of ~2.7 Mb/s. a) ll QKDchannel DatachannelsNo classical channel allocated
Multi-core fibre l l l
QKDchannel SRSDatachannel DetectedSRSFibrepropagation Filtering before detection b) QKD channel contamination from SRS c)d)e)
FIG. 4: General overview of co-existence of QKD and classical data channels over SDM fibres and key experiments. a)Wavelength channel allocation in a multi-core fibre. A wavelength is assigned to the QKD channel (in the centre core forexample, shown in orange), and has to be kept free in the adjacent cores (shaded blue) to prevent in-band inter-core crosstalk[93–96]. The other wavelengths in each core may be assigned to data channels. b) Spontaneous Raman scattering (SRS)generated when a classical channel is present in the same core can contaminate a QKD channel. Following propagation throughthe core of an MCF, SRS photons are produced from a classical channel (pump) over a broad wavelength range, eventuallybecoming strong noise to the QKD channel band. After the receiver’s filtering stage, the SRS photons are detected as an increasein the dark counts of the QKD system, lowering the generated secret key rate. c) Experiment demonstrating co-existence ofQKD and classical data over an MCF. Reprinted with permission from [93] [OSA]. d) Experimental demonstration of SRS overall cores of NT- and TA-MCFs. Reprinted with permission from [100]. e) Co-existence experiment of CV-QKD and classicalchannels over an MCF. Reprinted with permission from [97].
NT-MCF, as expected due to the higher cross-talk.Recently, improved classical channel data rates has been achieved over a 7-core fibre while simultaneously allocatingthe center core to a QKD channel [95]. Other works have also studied the use of a dedicated side-core for QKD whilehaving neighbouring cores filled with classical data [96], the inter-core crosstalk produced from classical channelson MCFs affecting continuous variable (CV) QKD systems [97] and performed detailed modelling on SDM-QKDintegration [98]. Finally, a major increase in key generation rate has been achieved by sending out parallel keys over37 cores of a MCF, while also propagating a 10Gbit/s data stream within each core, wavelength-multiplexed with theQKD channel [99]. One important limitation for co-existence is spontaneous Raman scattering (SRS), where photonsfrom classical channels are inelastically scattered over a broad wavelength range [90]. Even if the cross-talk producedfrom in-band photons can be fully removed (with high-quality filtering for instance), SRS photons will eventually bescattered back to the QKD channel band over the fibre link (Fig. 4b). Therefore, the overall system design needsto take this issue into account [91]. Recently, SRS has been demonstrated for the first time in each core of an MCF[100], indicating as expected the same limitations when simultaneously propagating quantum and classical signals inthe same core of an MCF. Table I lists relevant quantum information experiments using SDM fibres.
IV. OUTLOOK AND OPEN CHALLENGES
There has been a rapid acceptance of SDM fibres and devices by the quantum information community with promisingresults reported so far. On the one hand the ability of these fibres to successfully manipulate and propagate high-dimensional quantum states over long distances has proven very fruitful for quantum information processing. On theother hand, their use for a number of QI protocols will ease the integration of both quantum and classical networksystems based on the SDM optical fibre infrastructure.
Year Experiment Fibre type Distance Clock rate DOF Reference2012 Entanglement distribution FMF 40 cm ** Spatial [83]2013 Telecom integration FMF 2 m ** ** [92]2016 QKD + telecom integration 7-core MCF 53 km 10 Gb/s Time-bin [93]2017 HD-QKD 4-core MCF 300 m 1 kHz Path [70]2017 HD-QKD 7-core MCF (4 used) 3 m 5 kHz Path [71]2017 HD entanglement distribution 4-core MCF 30 cm ** Path [84]2017 Entanglement distribution FMF 1 km ** Polarisation/time-bin [86]2017 Parallel QKD 7-core MCF (4 used) 3 m 5 kHz Path [72]2018 QKD Ring-core 60 m ** OAM [73]2018 HD-QKD Ring-core 1.2 km 50 kHz OAM [74]2018 Telecom integration 7-core MCF 2.5 km ** ** [94]2018 Parallel QKD 37-core MCF 7.9 km 595 MHz Time-bin [99]2018 HD entanglement distribution FMF 1 km ** OAM [87]2019 HD entanglement distribution 4-core MCF 30 cm ** Path [85]2019 QKD + telecom integration 7-core MCF 1 km ** ** [95]2019 QKD + telecom integration 7-core MCF 30 km (attenuator) 50 MHz Time-bin [96]2019 Telecom integration 19-core MCF 10.1 km ** ** [97]2019 Telecom integration 7-core MCF 2.5 km ** ** [100]2019 HD entanglement distribution Ring-core 5 m ** Hybrid [97]2019 HD entanglement distribution FMF 250 m ** Hybrid [89]2019 MDI-QRNG 4-core MCF 45 cm 2 MHz Path [101]TABLE I: Quantum information experiments using SDM fibres. Telecom integration refers to experiments aimed at charac-terising the impact of classical data channels on a quantum channel over SDM fibres. The clock rate refers to the repetitionrates where active modulation was employed in the experiment. HD stands for high-dimensional, meaning that more than2 dimensional systems were used, and DOF for degree-of-freesom. MDI-QRNG stands for measurement device-independentquantum random number generation. ** means “not applicable” or no explicit information available.
Nevertheless, many challenges await that the community needs to handle to ensure that experiments based on SDMtechnology yield better results. Multi-core fibres have shown good promise for long-distance propagation and easeof integration with photonic circuits. Furthermore, high-quality devices can be built directly in the fibre itself [101].Next it is important to see if they can support propagation distances for high-dimensional states that is comparableto single-mode fibres (i.e. hundreds of kms). They also need to be validated for states of even higher dimensionality,by employing a fibre with a higher core number, such as 7 or 19. Regarding telecom compatibility, it is important toverify more stringent limits such as noise produced from non-linear effects such as Raman scattering and four-wavemixing produced from classical channels in different wavelengths from different cores.Although ring-core and even step-index fibres have also proved fruitful for OAM propagation, further experimentsneed to be carried out to verify their support for high-dimensions (only one experiment managed to go furtherthan OAM qubits, and even then only OAM qutrits were employed [87]). This is worth pursuing since experimentsin classical communications show that several modes can be simultaneously supported [102, 103], although MIMOdetection was still required, so better mode isolation will be needed for QC experiments. By far most OAM basedexperiments have resorted to bulk-optics-based mode sorters, although recent results open up a new path towardsintegration for OAM [28, 52]. FMFs also need to be studied in this regard, to verify their ability to coherentlypropagate superpositions of linearly polarised modes over long distances. The successful use of FMFs would open adirect path towards the transmission of much higher dimensional states, since they can be directly combined withMCFs. For instance, a fibre with 36 cores where each core supports the three lowest order LP modes, yielding apossible 108-dimensional space, has been demonstrated [104].An important challenge to be tackled comes from the modal dispersion. This problem is even more critical forentangled states due to their short coherence time. This has been tackled by pre-compensating the mode delay beforetransmission in the optical fibre [74, 87]. Further efforts need to be carried out to demonstrate feasibility over muchlonger distances, as well as ability to cover compensation for a wide range of modes, aiming at high-dimensionality.It is quite fortunate that the technological developments that are sustaining the growth of communication networkscan be directly applied for quantum information technologies. This has been the case since the dawn of photonicquantum information, and will continue to be so. We have highlighted here the key developments in the nascent inter-section of SDM and quantum information, with already many experiments having been able to directly benefit fromSDM. We envisage that (i) integration between SDM networks and quantum information systems will be inevitable,and (ii) SDM offers the hardware to support efficient, high-fidelity, high-dimensional quantum information processing,which will be a major cornerstone of future developments in quantum technologies.
Acknowledgements
G. X. acknowledges Ceniit Link¨oping University and the Swedish Research Council (VR 2017-04470) for financialsupport. G. L. acknowledges the support of Fondecyt 1160400, and Millennium Institute for Research in Optics,MIRO.
Author contributions
Both authors contributed equally to this manuscript.
Additional information
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