Improved parameter optimization method for measurement device independent protocol

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.