Quantum interference and coherence in one-dimensional disordered and localized quantum walk

TL;DR

This paper investigates how quantum interference and coherence influence the dynamics of one-dimensional disordered and localized quantum walks, enhancing understanding of localization phenomena and interference effects in quantum systems.

Contribution

It introduces a coherence measure to quantify quantum interference in discrete-time quantum walks, analyzing the roles of coherence in position and coin spaces for localization and disorder effects.

Findings

Coherence in position and coin spaces contributes to quantum interference.

Disorder and topological effects influence localization through interference.

Quantitative analysis differentiates types of localization mechanisms.

Abstract

One-dimensional discrete-time quantum walk has played an important role in development of quantum algorithms and protocols for different quantum simulations. The speedup observed in quantum walk algorithms is attributed to quantum interference and coherence of the wave packet in position space. Similarly, localization in quantum walk due to disorder is also attributed to quantum interference effect. Therefore, it is intriguing to have a closer look and understand the way quantum interference manifests in different forms of quantum walk dynamics. Quantum coherence in the system is responsible for quantum interference in the system. Here we will use coherence measure to quantify the interference in the discrete-time quantum walk. We show coherence in the position and coin space, together and independently, and present the contribution of coherence to the quantum interference in the system. This study helps us to differentiate the localization seen in one dimensional discrete-time quantum walks due to different forms of disorders and topological effects.