Channel loss seems to be the most severe limitation on the practical application of long
distance quantum key distribution. The idea of twin-field quantum key distribution can
improve the key rate from the linear scale of channel loss in the traditional decoy-state
method to the square root scale of the channel transmittance. However, the technical
demands are rather tough because they require single photon level interference of two
remote independent lasers. Here, we adopt the technology developed in the frequency and …

The sending-or-not-sending (SNS) protocol is one of the most major variants of the twin-field
(TF) quantum key distribution (QKD) protocol and has been realized in a 511-km field fiber,
the farthest field experiment to date. In practice, however, all decoy-state methods have
unavoidable source errors, and the source errors may be non-random, which compromises
the security condition of the existing TF-QKD protocols. In this study, we present a general
approach for efficiently calculating the SNS protocol's secure key rate with source errors, by …