Uniform stationary measure of space-inhomogeneous quantum walks in one dimension

Abstract

The discrete-time quantum walk (QW) is a quantum version of the random walk (RW) and has been widely investigated for the last two decades. Some remarkable properties of QW are well known. For example, QW has a ballistic spreading, i.e., QW is quadratically faster than RW. For some cases, localization occurs: a walker stays at the starting position forever. In this paper, we consider stationary measures of two-state QWs on the line. It was shown that for any space-homogeneous model, the uniform measure becomes the stationary measure. However, the corresponding result for space-inhomogeneous model is not known. Here, we present a class of space-inhomogeneous QWs on the line and cycles in which the uniform measure is stationary. Furthermore, we briefly discuss a difference between QWs and RWs.

arXiv comment9 pages

References in corpus (5)

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• Breakdown of an Electric-Field Driven System: a Mapping to a Quantum Walk
• Unveiling hidden topological phases of a one-dimensional Hadamard quantum walk
• The stationary measure of a space-inhomogeneous quantum walk on the line
• Stationary measures of three-state quantum walks on the one-dimensional lattice