Limit theorems for a localization model of 2-state quantum walks

Takuya Machida

Published 2010-08-06, updated 2011-06-22Version 2

We consider 2-state quantum walks (QWs) on the line, which are defined by two matrices. One of the matrices operates the walk at only half-time. In the usual QWs, localization does not occur at all. However, our walk can be localized around the origin. In this paper, we present two limit theorems, that is, one is a stationary distribution and the other is a convergence theorem in distribution.