Asymptotic Behavior Of Quantum Walks And Related Parameter Estimation

Quantum parameter estimation is an important method in quantum statistical theory,which is a natural crystallization of the cross fusion of quantum mechanics principle and classical statistical inference method.As an important representation of quantum walk,quantum states are used to describe the motion states of quantum particles(quantum walker).The estimation of quantum state needs to develop an estimation scheme that conforms to the principle of quantum mechanics.By estimating the parameters of quantum state,we can better understand the quantum state.The long time asymptotic behavior of quantum walk is the core topic of quantum walk theory.Its main concern is the localization of walk and the existence of uniform stationary measure.In this paper,the asymptotic behavior of several classes of space inhomogeneous quantum walk is studied by using the transfer matrix method,and the parameter estimation problem of three-state quantum walk with parameters is discussed.The main work is as follows:Firstly,a class of space inhomogeneous two-state quantum walk model is studied,the sufficient and necessary conditions of the localized existence and quantum state representations of one defect two-phase and multiple defects quantum walks are given.Secondly,the existence of uniform stationary measures for a class of space inhomogeneous one-dimensional three-state quantum walk is studied,and the corresponding existence results are obtained.In addition,it is proved that the quantum walk coin matrix has periodic representation.Finally,the quantum parameter estimation of one-dimensional three-state quantum walk with parameters is discussed and the corresponding quantum parameter estimation scheme is given.Furthermore,the unbiasedness and consistency of the estimation is verified.