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arXiv · 0903.4508

Limit theorems for discrete-time quantum walks on trees

Kota Chisaki·Masatoshi Hamada·Norio Konno·Etsuo Segawa
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Abstract

We consider a discrete-time quantum walk W_t given by the Grover transformation on the Cayley 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\to\infty, which corresponds to a localization in the case of an initial qubit state. The second one is X_t/t as t\to\infty, 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 Cayley tree.

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Kota Chisaki, Masatoshi Hamada, Norio Konno, Etsuo Segawa. 2009-03-26. Limit theorems for discrete-time quantum walks on trees. https://arxiv.org/abs/0903.4508

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