Asymmetric Channel Phase Matching Quantum Key Distribution

Abstract

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 symmetry in channel attenuation between communicating parties. In practice, channels used are often asymmetric due 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 impact 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 affecting 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 4dB. Although the decoy-state scheme cannot change the system's tolerance to channel attenuation differences, increasing the number of decoy states significantly improves system performance with a three-decoy-state phase-matching protocol outperforming a two-decoy-state protocol when the channel attenuation difference is large. Considering the limited data length, the system performance improves as the data length increases, and the tolerance to channel attenuation differences gradually increases. When the data length exceeds 10<sup>12</sup>, this improvement does not continue. The system cannot break through the boundary of linear key generation rate when the channel attenuation difference is 2dB and the data length is less than 10<sup>12</sup>. Compared to symmetric channels, the system performance improvement is more significant under asymmetric channel conditions as the data length increases.