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October, 2020 Space-homogeneous quantum walks on $\mathbb{Z}$ from the viewpoint of complex analysis
Hayato SAIGO, Hiroki SAKO
J. Math. Soc. Japan 72(4): 1201-1237 (October, 2020). DOI: 10.2969/jmsj/82648264

Abstract

The subject of this paper is quantum walks, which are expected to simulate several kinds of quantum dynamical systems. In this paper, we define analyticity for quantum walks on $\mathbb{Z}$. Almost all the quantum walks on $\mathbb{Z}$ which have been already studied are analytic. In the framework of analytic quantum walks, we can enlarge the theory of quantum walks. We obtain not only several generalizations of known results, but also new types of theorems. It is proved that every analytic space-homogeneous quantum walk on $\mathbb{Z}$ is essentially a composite of shift operators and continuous-time analytic space-homogeneous quantum walks. We also prove existence of the weak limit distribution for analytic space-homogeneous quantum walks on $\mathbb{Z}$.

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Hayato SAIGO. Hiroki SAKO. "Space-homogeneous quantum walks on $\mathbb{Z}$ from the viewpoint of complex analysis." J. Math. Soc. Japan 72 (4) 1201 - 1237, October, 2020. https://doi.org/10.2969/jmsj/82648264

Information

Received: 13 May 2019; Published: October, 2020
First available in Project Euclid: 17 August 2020

MathSciNet: MR4165930
Digital Object Identifier: 10.2969/jmsj/82648264

Subjects:
Primary: 46L99
Secondary: 60F05, 81Q99

Rights: Copyright © 2020 Mathematical Society of Japan

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Vol.72 • No. 4 • October, 2020
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