期刊
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
卷 55, 期 22, 页码 -出版社
IOP Publishing Ltd
DOI: 10.1088/1751-8121/ac6998
关键词
eigenvalues; quantum walks; localization; three-state quantum walks
This article introduces a method for finding the existence of eigenvalues in three-state quantum walks and uncovers the necessary and sufficient condition for the eigenvalue problem of a two-phase three-state quantum walk with one defect.
Mathematical analysis on the existence of eigenvalues is essential because it is deeply related to localization, which is an exceptionally crucial property of quantum walks (QWs). We construct the method for the eigenvalue problem via the transfer matrix for space-inhomogeneous three-state QWs in one dimension with a self-loop, which is an extension of the technique in a previous study (Kiumi and Saito 2021 Quantum Inf. Process. 20 171). This method reveals the necessary and sufficient condition for the eigenvalue problem of a two-phase three-state QW with one defect whose time evolution varies in the negative part, positive part, and at the origin.
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