Localization of space-inhomogeneous three-state quantum walks
Localization of space-inhomogeneous three-state quantum walks
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DOI：
10.1088/1751-8121/ac6998
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发表时间：
2022-06-07
影响因子：
2.1
通讯作者：
Kiumi, Chusei
中科院分区：
文献类型：
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作者：
Kiumi, Chusei
本征值的存在性的数学分析是必不可少的，因为它与局域化密切相关，而局域化是量子行走（QW）的一个非常重要的性质。我们通过一维空间非均匀三态量子阱的传输矩阵构造了本征值问题的方法，这是以前研究中技术的扩展（Kiumi和Saito 2021 Quantum Inf. Process. 20 171）。该方法揭示了具有一个缺陷的两相三态量子阱的本征值问题的充要条件，缺陷的时间演化在负部分、正部分和原点处都是变化的。
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.