  Quantum key distribution (QKD) offers a secret way to share keys between
legitimate users which is guaranteed by the law of quantum mechanics. Most
recently, the limitation of transmission distance without quantum repeaters was
broken through by twin-field QKD [Nature (London) 557, 400 (2018)]. Based on
its main idea, sending or not-sending (SNS) QKD protocol was proposed [Phys.
Rev. A 98, 062323 (2018)], which filled the remaining security loopholes and
can tolerate large misalignment errors. In this paper, we give a more general
model for SNS QKD, where the two legitimate users, Alice and Bob, can possess
asymmetric quantum channels. By applying the method present in the work, the
legitimate users can achieve dramatically increased key generation rate and
transmission distance compared with utilizing the original symmetric protocol.
Therefore, our present work represents a further step along the progress of
practical QKD.
