Sending-or-not-sending quantum key distribution with phase postselection

Quantum key distribution (QKD) could help to share secure key between two distant peers. In recent years, twin-field (TF) QKD has been widely investigated because of its long transmission distance. One of the popular variants of TF QKD is sending-or-not-sending (SNS) QKD, which has been experimentally verified to realize 1000-km level fibre key distribution. In this article, the authors introduce phase postselection into the SNS protocol. With this modification, the probability of selecting "sending" can be substantially improved. The numerical simulation shows that the transmission distance can be improved both with and without the actively odd-parity pairing method. With discrete phase randomization, the variant can have both a larger key rate and a longer distance.