A Spectral Analysis of Discrete-Time Quantum Walks Related to the Birth and Death Chains

被引：0

作者：

Choon-Lin Ho

Yusuke Ide

Norio Konno

Etsuo Segawa

Kentaro Takumi

机构：

[1] Tamkang University,Department of Physics

[2] Kanagawa University,Department of Information Systems Creation, Faculty of Engineering

[3] Yokohama National University,Department of Applied Mathematics, Faculty of Engineering

[4] Tohoku University,Graduate School of Information Science

来源：

Journal of Statistical Physics | 2018年 / 171卷

关键词：

Quantum walk; Birth and death chain; Ehrenfest model; Krawtchouk polynomials;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

In this paper, we consider a spectral analysis of discrete time quantum walks on the path. For isospectral coin cases, we show that the time averaged distribution and stationary distributions of the quantum walks are described by the pair of eigenvalues of the coins as well as the eigenvalues and eigenvectors of the corresponding random walks which are usually referred as the birth and death chains. As an example of the results, we derive the time averaged distribution of so-called Szegedy’s walk which is related to the Ehrenfest model. It is represented by Krawtchouk polynomials which is the eigenvectors of the model and includes the arcsine law.

引用

页码：207 / 219

页数：12

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