出版社：The Editorial Committee of the Interdisciplinary Information Sciences
摘要：We consider a discrete-time quantum walk Wt given by the Grover transformation on the homogeneous tree. We reduce Wt to a quantum walk Xt on a half line with a wall at the origin. This paper presents two types of limit theorems for Xt . The first one is Xt as t →∞, which corresponds to a localization in the case of an initial qubit state. The second one is Xt ⁄ 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
