Localization of a multi-dimensional quantum walk with one defect

被引：0
|
作者：
Toru Fuda
Daiju Funakawa
Akito Suzuki
机构：
[1] Hokkaido University,Department of Mathematics
[2] Shinshu University,Division of Mathematics and Physics, Faculty of Engineering
来源：
Quantum Information Processing | 2017年 / 16卷
关键词：
Quantum walks; Localization; Eigenvalues; Feshbach map;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, we introduce a multi-dimensional generalization of Kitagawa’s split-step discrete-time quantum walk, study the spectrum of its evolution operator for the case of one-defect coins, and prove localization of the walk. Using a spectral mapping theorem, we can reduce the spectral analysis of the evolution operator to that of a discrete Schrödinger operator with variable coefficients, which is analyzed using the Feshbach map.
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