Sending-or-not-sending twin-field quantum key distribution with advantage distillation

A sending-or-not-sending (SNS) protocol is a very promising variant in twin-field quantum key distribution (TFQKD) for its advantages at the regime of long distance and the robustness against large optical misalignment. The actively odd-parity pairing (AOPP) method can significantly enhance the key-rate performance of the original SNS TFQKD, which forms the AOPP SNS TFQKD protocol. In this paper, we introduce the advantage distillation (AD) method to further improve the communication distance for AOPP SNS TFQKD. We also prove the composable security against coherent attacks for the AOPP SNS TFQKD with AD in the finite-key regime for bit blocks with a size of 2 in the AD process. Our AD method for AOPP SNS TFQKD protocol is expected to improve the key-rate performance in practice without changing the SNS TFQKD experimental system.