文章基本信息

标题：Limit Theorems for Discrete-Time Quantum Walks on Trees
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作者：Kota CHISAKI ; Masatoshi HAMADA ; 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：2009
卷号：15
期号：3
页码：423-429
DOI：10.4036/iis.2009.423
出版社：The Editorial Committee of the Interdisciplinary Information Sciences
摘要：We consider a discrete-time quantum walk W_t given by the Grover transformation on the homogeneous tree. We reduce W_t to a quantum walk X_t on a half line with a wall at the origin. This paper presents two types of limit theorems for X_t . The first one is X_t as t →∞, which corresponds to a localization in the case of an initial qubit state. The second one is X_t ⁄ t as t →∞, whose limit density is given by the Konno density function [1–4]. The density appears in various situations of discrete-time cases. The corresponding similar limit theorem was proved in [5] for a continuous-time case on the homogeneous tree.
关键词：Quantum walk;homogeneous tree;Limit theorem;Konno density function