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.
Twin-field quantum key distribution (TF-QKD) has attracted considerable attention and developed rapidly due to its ability to surpass the fundamental rate-distance limit of QKD. However, the device imperfections may compromise its practical implementations. The goal of this paper is to make it robust against the state preparation flaws (SPFs) and side channels at the light source. We adopt the sending or not-sending (SNS) TF-QKD protocol to accommodate the SPFs and multiple optical modes in the emitted states. We analyze that the flaws of the phase modulation can be overcome by regarding the deviation of the phase as phase noise and eliminating it with the post-selection of phase. To overcome the side channels, we extend the generalized loss-tolerant (GLT) method to the four-intensity decoy-state SNS protocol. Remarkably, by decomposing of the two-mode single-photon states, the phase error rate can be estimated with only four parameters. The practical security of the SNS protocol with flawed and leaky source can be guaranteed. Our results might constitute a crucial step towards guaranteeing the practical implementation of the SNS protocol.
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