Parameters In Quantum Walks And Their Estimations

Quantum statistics is the natural product of the combination and cross pene-tration of quantum mechanics theory and classical statistical methods.As a branch of quantum statistics,quantum parameter estimation theory is mainly studied quan-tum walk is the quantum analogue of classical random walk,which has a wide range of applications in quantum information theory,quantum computing and other fields.In this paper,we mainly discuss the parameter estimation in quantum walk.The main work is as follows.Firstly,a one-dimensional unitary quantum walk model with parameters in discrete time(for short W-Y quantum walk with parameters)is proposed by using quantum Bernoulli noise.The basic properties of this model are investigated.Secondly,the probability distribution of the W-Y quantum walk with param-eters in a class of initial states is obtained.It is found that the parameters have no significant effect on the probability distribution of the walking.Thirdly,for a class of one-dimensional two-state quantum walk with parame-ters,the corresponding quantum parameter estimation problem is discussed,a spe-cific parameter estimation scheme is proposed,and it is proved that the estimation scheme is unbiased and consistent.