Memory-assisted quantum key distribution aims to use existing quantum-device technologies to offer rate-versus-distance enhancements. Here, a variant of such systems, relying on single-photon sources, is proposed that counters the multiple-excitation effects in ensemble-based memories

Lo Piparo, N

Razavi, M

White Rose Research Online

This is a repository copy of Memory-Assised Quantum Key Distribution Immune to Multiple-Excitation Effects.White Rose Research Online URL for this paper:http://eprints.whiterose.ac.uk/113657/Version: Accepted VersionProceedings Paper:Lo Piparo, N and Razavi, M (2016) Memory-Assised Quantum Key Distribution Immune to Multiple-Excitation Effects. In: Lasers and Electro-Optics (CLEO), 2016 Conference on. 2016 Conference on Lasers and Electro-Optics (CLEO), 05-10 Jun 2016, California, USA. IEEE . ISBN 978-1-5090-2434-6 © 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising orpromotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.eprints@whiterose.ac.ukhttps://eprints.whiterose.ac.uk/Reuse Unless indicated otherwise, fulltext items are protected by copyright with all rights reserved. The copyright exception in section 29 of the Copyright, Designs and Patents Act 1988 allows the making of a single copy solely for the purpose of non-commercial research or private study within the limits of fair dealing. The publisher or other rights-holder may allow further reproduction and re-use of this version - refer to the White Rose Research Online record for this item. Where records identify the publisher as the copyright holder, users can verify any specific terms of use on the publisher’s website. Takedown If you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing eprints@whiterose.ac.uk including the URL of the record and the reason for the withdrawal request. Memory-Assisted Quantum Key Distribution Immune toMultiple-Excitation EectsNicoló Lo Piparo1 and Mohsen Razavi11School of Electronic and Electrical Engineering, University of Leeds, Leeds, UK1Woodhouse Lane, Leeds, LS2 9DX, UK. Tel.:+44 0113 3432082 - email: eennl@leeds.ac.ukAbstractMemory-assisted quantum key distribution aims to use existing quantum-device technolo-gies to oer rate-versus-distance enhancements. Here, a variant of such systems, relying onsingle-photon sources, is proposed that counters the multiple-excitation eects in ensemble-based memories.Long-distance quantum communications (LDQC) has a fundamental role in sharing secure informa-tion in future quantum networks. The key solution to trust-free LDQC relies on quantum repeaters.However, the demanding requirements for the implementation of the repeater systems do not allowan immediate use of such a technology. Here, we present a simple solution based on memory-assisted measurement-device-independent quantum key distribution (MA-MDI-QKD) structure [1]that can improve the rate-versus-distance behavior using state-of-the-art devices. Our proposal alsoremedies the multiple-excitation errors that could preclude ensemble-based memories from beingused in such structures [2].MA-MDI-QKD resembles a single-node quantum repeater with quantum memories (QMs) only inthe middle; see Fig. 1(a) for the dual-rail phase-encoded setup. In this scheme, both users send asingle photon, which has been encoded in one of the four BB84 states, to a middle station. Thephoton interacts with another photon entangled with the QMs in a side Bell-state measurement(BSM) module. If a side-BSM is successful, the state sent by the user is ideally teleported intothe QMs. Once all QMs are loaded with the relevant states, they are read and a central-BSM isperformed on the retrieved photons, creating, thus, correlated keys among users. The QMs in usemust meet certain criteria, such as having a high bandwidth-storage product and fast entanglingtimes [1], where both these conditions are met by ensemble-based QMs [1]. The conventionalentangling procedure for such QMs will however lead to multiple excitations, which have beenshown to be detrimental for the performance of the system [2].In this paper, we propose to use single-photon sources (SPSs) in order to generate entangled photons.Figure 1(b) shows the dual-rail phase-encoded version of our proposed MA-MDI-QKD system, whereFigure 1: (a) MA-MDI-QKD scheme with indirectly heralding QMs [1]. (b) The proposed scheme with theproposed scheme relying on quasi-EPR module as sketched in (c). (d) The nominal values of the parameters used.1Figure 2: Key rates of the system in Fig. 1(b). In (a), key rate per pulse is compared with the upper bound in [3].In (b) we consider the key rate in b/s with a the repetition rate of 1 GHz for dierent values of the coherence timeT1 compared with the no-memory MDI-QKD system. The same value of 200 ps has been used for the writing time,reading time, and duration of the pulse as reported in [4].the entangling operation is done in the boxes labeled quasi-EPR. The architecture of this module isdepicted in Fig. 1(c). Here, two SPSs each generate ideally one photon that interfere at four 50:50beam splitters. The interaction pattern illustrated in Fig. 1(c) will create an entangled photon pairplus some spurious terms. These spurious terms include four two-photon Fock states, each at everyoutput of Fig. 1(c). In the case of the entangled states, one half will be directed towards the BSMmodules and the other half to the QMs, where the latter will be stored into the QMs. Here, weassume that our employed SPS has generated at most one photon, because of which we normallyavoid generating multiple excitations in the QMs.In order to evaluate the performance of our proposed system, we calculate the secret key rate forthe setup of Fig. 1(b) by considering the main setup's ineciencies as listed in Fig. 1(d). Figure2(a) compares the secret key rate per pulse of the setup of Fig. 1(b) with the upper bound for ano-repeater QKD system reported in [3]. We can see that the key rate of our setup outperformsthis bound around above 200 km. We can deduce that the eect of the spurious terms in the outputstate created by quasi-EPR modules is not detrimental for the overall performance of the system.That is due to the fact that when the two-photon Fock states generated by the quasi-EPR modulesare directed towards the QMs, no photons will interact with the state sent by the users. Therefore,the side-BSM can be successful only through a dark count event. Similarly, when the two-photonFock states are directed towards the side-BSM, a vacuum state will be loaded into the QMs, whichwould not result in a successful central-BSM, unless again because of the dark count. With a darkcount rate as low as 10−9/s, the corresponding errors will be low at short-to-moderate distances.We also consider the total key rate in b/s by assuming a repetition rate of 1 GHz, and for dierentvalues of the amplitude decay time constant, T1. Figure 2(b) shows that our setup outperforms theno-memory system [5] at a distance L ∼ 190 km for a coherence time as low as to T1 = 1 µs.The required specications of our proposed system is within reach of existing technologies. Ensemble-based memories have shown to have fast writing times, needed for high repetition rate, on the orderof 200 ps, and coherence times on the order of 1 µs. SPSs based on quantum dots in photonicnanowires, also reach an eciency of 0.72 [6] and are known to have very low two-photon compo-nents. With such state-of-the-art devices our scheme leads to two order of magnitude improvementat distances over 300 km, over existing no-memory QKD systems. This sets an achievable interme-diate milestone for LDQC. This work was partly funded by UK's EPSRC Grant EP/M013472/1.References[1] C Panayi, M. Razavi, X. Ma, and N. Lütkenhaus. New. J. Phys., 16:043005, 2013.[2] N. Lo Piparo, M. Razavi, and C. Panayi. IEEE J. of selected topics in quantum electron.,21:6601010, May/June 2015.[3] S. Pirandola, R. Laurenza, C. Ottaviani, and L. Banchi. arXiv:1510.08863, 2015.[4] X.-H. Bao and et al. Nat. Phys., 8:517521, 2012.[5] H.-K. Lo, M. Curty, and B. Qi. Phys. Rev. Lett., 108:130503, Mar 2012.[6] J. Caudon and et al. Nat. Photon., 4:174177, 2010.2

Memory-Assised Quantum Key Distribution Immune to Multiple-Excitation Effects

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Memory-Assised Quantum Key Distribution Immune to Multiple-Excitation Effects

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