Asymmetric channel phase matching quantum key distribution

The phase-matching protocol is a practical and promising protocol that can surpass the linear key generation rate boundary. However, classical phase-matching quantum key distribution requires the channel attenuation between communicating parties to be symmetric. In practice, channels used are often asymmetric, owing to geographical reasons in a quantum key distribution network. To enhance the practicality of phase matching, this paper proposes an asymmetric phase-matching protocol based on the classical framework and establishes a relevant mathematical simulation model to study the influence of channel asymmetry on its performance. The simulation results show that channel asymmetry significantly affects the count rate, error rate, gain, and quantum bit error rate (QBER), ultimately, system performance. As the channel attenuation difference increases, the system performance decreases and the rate of decrease accelerates. Key generation becomes impossible when the channel attenuation difference exceeds 4 dB. Although the decoy-state scheme cannot change the system's tolerance to channel attenuation difference, when the channel attenuation difference is large, the increasing of the number of decoy states significantly can improve system performance, with a three-decoy-state phase-matching protocol outperforming a two-decoy-state protocol. Considering the limited data length, the system performance is improved as the data length increases, and the tolerance to channel attenuation differences gradually increases. When the data length exceeds 1012, this improvement does not continue any more. The system cannot break through the boundary of linear key generation rate when the channel attenuation difference is 2 dB and the data length is less than 1012. Comparing with symmetric channels, the system performance improvement is very significant under asymmetric channel conditions as the data length increases.