%0 Journal Article
%T The non-uniform stationary measure for discrete-time quantum walks in one dimension
%A Norio Konno
%A Masato Takei
%J Mathematics
%D 2014
%I arXiv
%X We consider stationary measures of the one-dimensional discrete-time quantum walks (QWs) with two chiralities, which is defined by a 2 times 2 unitary matrix U. In our previous paper [15], we proved that any uniform measure becomes the stationary measure of the QW by solving the corresponding eigenvalue problem. This paper reports that non-uniform measures are also stationary measures of the QW except U is diagonal. For diagonal matrices, we show that any stationary measure is uniform. Moreover, we prove that any uniform measure becomes a stationary measure for more general QWs not by solving the eigenvalue problem but by a simple argument.
%U http://arxiv.org/abs/1410.7651v1