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.
The optimal selection of parameters in practical quantum key distribution can greatly improve the key generation rate and maximum transmission distance of the system. Due to the high cost of global search algorithm, local search algorithm is widely used. However, there are two vulnerabilities in local search algorithm, one is that the solution obtained is not always the global optimal solution, the other is that the effectiveness of the algorithm is greatly dependent on the choice of initial value. It is different from the previous article that this paper uses the Monte Carlo method to prove whether the key generation rate function is convex, and also simulates and analyzes the projection of key generation rate function on each dimension of the parameter. In order to eliminate the effect of the initial value, this paper proposes the particle swarm local search optimization algorithm which is combining particle swarm optimization algorithm and local search algorithm. The first step is using the particle swarm optimization to find a valid parameter which leads to nonzero key generation rate, the second step is using the parameter as the initial value of local search algorithm to derive the global optimal solution. Then, the two algorithms are simulated and compared. The results show that the key generation rate function is non-convex because it does not satisfy the definition of a convex function, however, since the key generation rate function has only one non-zero stagnation point, the LSA algorithm can still obtain the global optimal solution with a proper initial value, when the transmission distance is relatively long, the local search algorithm is invalid because it is difficult to obtain an effective initial value by random value method. Particle swarm optimization algorithm can overcome this shortcoming and improve the maximum transmission distance of the system at the cost of slightly increasing the complexity of the algorithm.
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