Limit theorems of a 3-state quantum walk and its application for discrete uniform measures

Abstract

We present two long-time limit theorems of a 3-state quantum walk on the line when the walker starts from the origin. One is a limit measure which is obtained from the probability distribution of the walk at a long-time limit, and the other is a convergence in distribution for the walker's position in a rescaled space by time. In addition, as an application of the walk, we obtain discrete uniform limit measures from the 3-state walk with a delocalized initial state.

arXiv commentQuantum Information and Computation, Vol.15 No.5&6, pp.406-418 (2015)

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