Repeated measurements and random scattering in quantum walks

TL;DR

This paper investigates how random scattering and repeated measurements influence quantum walks on finite graphs, revealing that localization effects can restrict transitions and create dark states, thus offering tools for quantum walk control.

Contribution

It introduces a constructive approach using localized and delocalized bases to analyze the effects of random scattering and measurements on quantum walks, highlighting their role in control.

Findings

Localization restricts transition probabilities

Dark states emerge in monitored evolution

Both scattering and measurements are effective control tools

Abstract

We study the effect of random scattering in quantum walks on a finite graph and compare it with the effect of repeated measurements. To this end, a constructive approach is employed by introducing a localized and a delocalized basis for the underlying Hilbert space. This enables us to design Hamiltonians whose eigenvectors are either localized or delocalized. By presenting some specific examples we demonstrate that the localization of eigenvectors restricts the transition probabilities on the graph and leads to dark states in the monitored evolution. We conclude that repeated measurements as well as random scattering provide efficient tools for controlling quantum walks.