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Effect of polarization mismatch on differential phase based measurement device independent quantum key distribution

Nilesh Sharma, Chandrashekar Radhakrishnan, Anil Prabhakar

Published Jan 1, 2023• 0 citations
Publisher

Abstract

The effect of polarization mismatched coherent pulses on the key rates of differential phase based MDI QKD is investigated. It is found that this protocol can withstand a polarization mismatch of at most 11°.
DOI
10.1364/quantum.2023.qtu3a.39

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The ideal measurement-device-independent quantum key distribution (MDI-QKD), which is immune to all detector side-channel attacks, is built on the Bell state measurement of two single-photon states. However, in practical MDI-QKD where phase-randomized weak coherent pulses (PR-WCPs) are used, the mismatch between states preparation and measurement in X basis leads to the bit error rate of more than 25%, which poses a challenge to the security of QKD. In this paper, we provide a security analysis of practical MDI-QKD based on polarization coding. We analyze the Hong-Ou-Mandel interference of PR-WCPs and Poisson-distributed photon number states (PNs), and find that these two sources are equivalent in MDI-QKD. The security analysis based on entanglement distillation is carried out on PNs, and the measurement results in Z basis and X basis are averaged to overcome the noncorrelation of the error rates in these two bases. Compared with GLLP scheme, a tighter key rate is obtained in this work, and the key rate deviates from the linear key rate bound in a short distance due to the finite proportion of multiphoton terms.
Measurement-Device-Independent Quantum Key Distribution (MDI-QKD) enhances security by removing vulnerabilities associated with detector side channels. Real-world implementations of measurement device independent (MDI) QKD face practical challenges such as channel asymmetry and physical imperfections, which degrade the visibility of Hong-Ou-Mandel (HOM) interference, an essential factor in determining the secure key rate. In this work, we evaluate the performance of differential phase encoded (DPE) MDI-QKD under realistic, asymmetric conditions. We analyse the effects of polarisation and pulse-width mismatches caused by channel asymmetry and identify tolerable limits for secure key generation. We introduce a plug-and-play DPE-MDI-QKD architecture that mitigates polarisation fluctuations using Faraday mirrors and also compensates for pulse-width mismatches. Furthermore, we propose an improved sifting scheme that raises the sifting efficiency from49\frac{4}{9}94​to23\frac{2}{3}32​, improving the secure key generation rates by 50% and making it especially suitable for plug-and-play systems. These results offer practical insights into enhancing the robustness and efficiency of DPE-MDI-QKD, enabling more secure quantum communication over imperfect and asymmetric quantum channels.
This paper proposes a measurement-device-independent quantum key distribution (MDI-QKD) scheme based on differential phase encoding. The differential phase shift MDI-QKD (DPS-MDI-QKD) couples the advantages of DPS-QKD with that of MDI-QKD. The proposed scheme offers resistance against photon number splitting attack and phase fluctuations as well as immunity against detector side-channel vulnerabilities. The design proposed in this paper uses weak coherent pulses in a superposition of three orthogonal states, corresponding to one of three distinct paths in a delay-line interferometer. The classical bit information is encoded in the phase difference between pulses traversing successive paths. This 3-pulse superposition offers enhanced security compared to using a train of pulses by decreasing the learning rate of an eavesdropper and unmasking her presence with an increased error rate upon application of intercept and resend attack and beamsplitter attack. The proposed scheme employs phase locking of the sources of the two trusted parties so as to maintain the coherence between their optical signal, and uses a beamsplitter (BS) at the untrusted node (Charlie) to extract the key information from the phase encoded signals.
We demonstrate the first implementation of polarization encoding measurement-device-independent quantum key distribution (MDI-QKD), which is immune to all detector side-channel attacks. Active phase randomization of each individual pulse is implemented to protect against attacks on imperfect sources. By optimizing the parameters in the decoy state protocol, we show that it is feasible to implement polarization encoding MDI-QKD with commercial off-the-shelf devices. A rigorous finite key analysis is applied to estimate the secure key rate. Our work paves the way for the realization of a MDI-QKD network, in which the users only need compact and low-cost state-preparation devices and can share complicated and expensive detectors provided by an untrusted network server.
The source flaw associated with the basis vector in the reference-frame-independent measurement-device-independent quantum key distribution (RFI-MDI-QKD) has not been systematically studied. As a result, it is often assumed that bit error is equal to phase error, which is not theoretically rigorous. Here, we propose a postprocessing method to estimate the phase error rate from the discarded mismatched-basis statistics, where the qubit source does not need to be characterized in detail. The source flaw in the basis vector of the RFI-MDI-QKD protocol can thus be corrected using this method. The numerical simulation results clearly demonstrate that the RFI-MDI-QKD protocol with uncharacterized sources is also insensitive to the misalignment of the reference frame.