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Chinese Physics Letters

Parameters Optimization of Decoy-State Phase-Matching Quantum Key Distribution Based on the Nature-Inspired Algorithms

Chang 畅 Liu 刘, Yue 悦 Li 李, Haoyang Wang, Kaiyi Shi, Duo Ma, Yujia Zhang, Haiqiang Ma

Published Dec 9, 2024• 3 citations

Abstract

Abstract Phase-matching quantum-key distribution (PM-QKD) has achieved significant results in various practical applications. However, real-time communication requires dynamic adjustment and optimization of key parameters during communication. In this letter, we predict the PM-QKD parameters using nature-inspired algorithms (NIAs). The results are obtained from an exhaustive traversal algorithm (ETA), which serves as a benchmark. We mainly study the parameter optimization effects of the two NIAs: ant colony optimization (ACO) and the genetic algorithm (GA). The configuration of the inherent parameters of these algorithms in the decoy-state PM-QKD is also discussed. The simulation results indicate that the parameters obtained by the ACO exhibit superior convergence and stability, whereas the GA results are relatively scattered. Nevertheless, more than 97% of the key rates predicted by both algorithms are highly consistent with the optimal key rate. Moreover, the relative error of the key rates remained below 10%. Furthermore, NIAs maintain power consumption below 8 W and require three orders of magnitude less computing time than ETA.

DOI: 10.1088/0256-307x/42/1/010301

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The phase-matching quantum key distribution (PM-QKD), one of the variants of Twin-Field (TF) QKD protocol, was recently proposed to overcome the rate-distance limits of point to point protocol without quantum repeaters. In this paper, we propose a more practical PM-QKD protocol version with four-intensity decoy states and source errors, since neither the infinite decoy states nor the precise control of the light source is available in practice. We present the formulation of the secure key rate of the proposed protocol and analyze the performances of the protocol with and without source errors by numerical simulations.

The twin-field quantum key distribution (TF-QKD) protocol and its variations have been proposed to overcome the linear Pirandola-Laurenza-Ottaviani-Banchi (PLOB) bound. One variation called phase-matching QKD (PM-QKD) protocol employs discrete phase randomization and the phase post-compensation technique to improve the key rate quadratically. However, the discrete phase randomization opens a loophole to threaten the actual security. In this paper, we first introduce the unambiguous state discrimination (USD) measurement and the photon-number-splitting (PNS) attack against PM-QKD with imperfect phase randomization. Then, we prove the rigorous security of decoy state PM-QKD with discrete phase randomization. Simulation results show that, considering the intrinsic bit error rate and sifting factor, there is an optimal discrete phase randomization value to guarantee security and performance. Furthermore, as the number of discrete phase randomization increases, the key rate of adopting vacuum and one decoy state approaches infinite decoy states, the key rate between discrete phase randomization and continuous phase randomization is almost the same.

The twin-field quantum key distribution (TF-QKD) protocol has been studied widely to overcome the linear bound, and several variations of the TF-QKD protocol have been proposed to improve security and practicality. One variation called the phase-matching QKD (PM-QKD) protocol develops an optical-mode-based security; simultaneously, it has a quadratic improvement of key rate without either basis choice or phase locking. So far, the main research work of the PM-QKD protocol has focused on symmetric channels. However, it is quite common that the two channels have asymmetric transmittances in real life. In this paper, we discuss the effects of asymmetric channels on the PM-QKD protocol; to reach a much better performance and achieve a higher key rate, the intensity must be optimized to compensate for channel asymmetry. We also study the practical issues of finite-key effects and intensity fluctuations, which have significant effects on the key rate of PM-QKD.

Aiming at the shortcoming of ant colony optimization which was only suitable for the discrete optimization and the problem of slow convergence,this paper proposed a suitable quantum ant colony optimization algorithm for continuous optimization. The locations of ant were directly encoded by the phase of qubits in the proposed algorithm. First,determined the destination to move according to the select probability constructed by the pheromone information and heuristic information,and then updated the qubits of ant by quantum rotation gates to achieve ant moving,and mutated by quantum Pauli-Z gates to increase diversity of ants. Finally,updated the pheromone information and the heuristic information in the new location of ants. As performed the optimization in [0,2π]n ,which had nothing to do with the specific issues,hence,the proposed method had good adaptability for a variety of optimization problems. With applications of function extremum and controller parameters optimization,the simulation results show that the proposed algorithm is superior to the continuous quantum ant colony algorithm and the standard genetic algorithm in both search capability and optimization efficiency.

Abstract Phase-matching quantum key distribution (PM-QKD) provides a promising solution to surpass the fundamental rate–distance bound without quantum repeaters. In this paper, we insert an additional advantage distillation (AD) step after quantum communication to improve the performance of PM-QKD. Simulation results show that, by splitting the raw key into blocks of only a few bits so as to identify highly correlated bit pairs, the AD method can tolerate high system misalignment errors and improve the secret key rate and transmission distance significantly, which is very promising in current PM-QKD systems.