Extraordinary behaviors in two-dimensional decoherent alternative quantum walk

TL;DR

This paper analyzes how decoherence affects two-dimensional alternative quantum walks, revealing anisotropic behaviors and correlations that differ from classical and purely quantum dynamics.

Contribution

It provides analytic expressions for moments of position distribution in 2D AQW under decoherence and explores anisotropic effects and correlations.

Findings

Decoherence causes anisotropic position distributions.

Not all quantum walks transition to classical behavior under decoherence.

Anisotropic correlations between walkers and coin are observed.

Abstract

The quantum and classical behaviors of two-dimensional (2D) alternative quantum walk (AQW) in the presence of decoherence have been discussed in detail. For any kinds of decoherence, the analytic expressions for the moments of position distribution of AQW have been obtained. Taking the broken line noise and coin-decoherence as examples of decoherence, we find that when the decoherence only emerges in one direction, the anisotropic position distribution pattern appears, and not all the motions of quantum walkers exhibit the transition from quantum to classical behaviors. The correlations between the walkers and the coin in 2D AQW have been discussed. The anisotropic correlations between walkers and coin have been revealed in the presence of decoherence.