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Limit theorems for a localization model of 2-state quantum walks (1008.1116v2)
Published 6 Aug 2010 in quant-ph
Abstract: 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.