文章基本信息

标题：The Stationary Measure for Diagonal Quantum Walk with One Defect
本地全文：下载
作者：Takako ENDO ; Hikari KAWAI ; Norio KONNO 等
期刊名称：Interdisciplinary Information Sciences
印刷版ISSN：1340-9050
电子版ISSN：1347-6157
出版年度：2017
卷号：23
期号：1
页码：57-64
DOI：10.4036/iis.2017.A.08
出版社：The Editorial Committee of the Interdisciplinary Information Sciences
摘要：This study is motivated by the previous work [14]. We treat 3 types of the one-dimensional quantum walks (QWs), whose time evolutions are described by diagonal unitary matrices except at one defected point. In this paper, we call the QW defined by diagonal unitary matrices, ``the diagonal QW'', and we consider the stationary distributions of general 2-state diagonal QW with one defect, 3-state space-homogeneous diagonal QW, and 3-state diagonal QW with one defect. One of the purposes of our study is to characterize the QWs by the stationary measure, which may lead to answer the basic and natural question, ``What are stationary measures for one-dimensional QWs?''. In order to analyze the stationary distribution, we focus on the corresponding eigenvalue problems and the definition of the stationary measure.
关键词：space-homogeneous quantum walk;space-inhomogeneous quantum walk;stationary distribution;generating function;classification