The defect-induced localization in many positions of the quantum random walk

TL;DR

This paper investigates how introducing a phase defect at various positions in a quantum random walk causes localization of the probability distribution, with localization behavior depending on the defect position and coin operator.

Contribution

It reveals the position-dependent localization phenomena in quantum random walks caused by phase defects and their dependence on the coin operator, providing new insights into quantum walk dynamics.

Findings

Localization occurs at defect positions in QRW.

Localized probability amplitude depends on defect position.

Localization amplitude shows non-trivial dependence on coin operator.

Abstract

We study the localization of probability distribution in a discrete quantum random walk on an infinite chain. With a phase defect introduced in any position of the quantum random walk (QRW), we have found that the localization of the probability distribution in the QRW emerges. Different localized behaviors of the probability distribution in the QRW are presented when the defect occupies different positions. Given that the coefficients of the localized stationary eigenstates relies on the coin operator, we reveal that when the defect occupies different positions, the amplitude of localized probability distribution in the QRW exhibits a non-trivial dependence on the coin operator.