Limit theorems for a localization model of 2-state quantum walks
arXiv:1008.1116 · doi:10.1142/S0219749911007460
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.
International Journal of Quantum Information, Vol.9, No.3, pp.863-874 (2011)