Abstract
The twin-field quantum key distribution (TF-QKD) protocol and its variations have been proposed to overcome the linear Pirandola–Laurenza–Ottaviani–Banchi (PLOB) bound. One variation called phase-matching QKD (PM-QKD) protocol employs discrete phase randomization and the phase post-compensation technique to improve the key rate quadratically. However, the discrete phase randomization opens a loophole to threaten the actual security. In this paper, we first introduce the unambiguous state discrimination (USD) measurement and the photon-number-splitting (PNS) attack against PM-QKD with imperfect phase randomization. Then, we prove the rigorous security of decoy state PM-QKD with discrete phase randomization. Simulation results show that, considering the intrinsic bit error rate and sifting factor, there is an optimal discrete phase randomization value to guarantee security and performance. Furthermore, as the number of discrete phase randomization increases, the key rate of adopting vacuum and one decoy state approaches infinite decoy states, the key rate between discrete phase randomization and continuous phase randomization is almost the same.
Highlights
Quantum key distribution (QKD) can offer information theoretically secure means to distribute secret keys between two remote parties [1], but the performance is restricted by the fundamental rate-loss limit [2,3]
The other one is to actively modulate the phase of coherent sources controlled by a phase modulator with a true random number generator; this method is suitable for phase-matching QKD (PM-QKD), but the phase randomization is not continuous
Uses a different security poof method with Reference [8], and there is no in-depth formula derivation in the decoy state PM-QKD with discrete phase randomization. We focus on these discrete global phase randomization issues in the PM-QKD protocol [39], study a concrete attack against PM-QKD with imperfect phase randomization, apply the decoy-state method to derive the single photon yield formula to exhibit performance of the key rate and compare the yield difference of continuous phase randomization with discrete phase randomization
Summary
Quantum key distribution (QKD) can offer information theoretically secure means to distribute secret keys between two remote parties [1], but the performance is restricted by the fundamental rate-loss limit [2,3]. The other one is to actively modulate the phase of coherent sources controlled by a phase modulator with a true random number generator; this method is suitable for PM-QKD, but the phase randomization is not continuous Neither of these two means satisfy the assumption of the decoy state method, which may introduce a potential loophole that threatens the security of the actual protocol [30]. We focus on these discrete global phase randomization issues in the PM-QKD protocol [39], study a concrete attack against PM-QKD with imperfect phase randomization, apply the decoy-state method to derive the single photon yield formula to exhibit performance of the key rate and compare the yield difference of continuous phase randomization with discrete phase randomization.
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