Disorder induced localization and enhancement of entanglement in one- and two-dimensional quantum walks

TL;DR

This paper investigates how disorder affects quantum walks in one- and two-dimensional systems, revealing localization effects and varied entanglement behaviors, with implications for quantum information processing.

Contribution

It demonstrates that disorder induces localization in quantum walks and shows that entanglement can be either decreased or enhanced depending on the type of disorder introduced.

Findings

Disorder causes localization in quantum walks.

Spatial disorder decreases entanglement; temporal and spatio-temporal disorder can enhance it.

The results suggest potential for disorder-controlled quantum information applications.

Abstract

The time evolution of one- and two-dimensional discrete-time quantum walk with increase in disorder is studied. We use spatial, temporal and spatio-temporal broken periodicity of the unitary evolution as disorder to mimic the effect of disordered/random medium in our study. Disorder induces a dramatic change in the interference pattern leading to localization of the quantum walks in one- and two-dimensions. Spatial disorder results in the decreases of the particle and position entanglement in one-dimension and counter intuitively, an enhancement in entanglement with temporal and spatio-temporal disorder is seen. The study signifies that the Anderson localization of quantum state without compromising on the degree of entanglement could be implement in a large variety of physical settings where quantum walks has been realized. The study presented here could make it feasible to explore, theoretically and experimentally the interplay between disorder and entanglement. This also brings up a variety of intriguing questions relating to the negative and positive implications on algorithmic and other applications.