One-Dimensional Three-State Quantum Walk with Single-Point Phase Defects

Abstract

In this paper, we study a three-state quantum walk with a phase defect at a designated position. The coin operator is a parametrization of the eigenvectors of the Grover matrix. We numerically investigate the properties of the proposed model via the position probability distribution, the position standard deviation, and the time-averaged probability at the designated position. It is shown that the localization effect can be governed by the phase defect’s position and strength, coin parameter and initial state.