Phase transition of an open quantum walk

TL;DR

This paper investigates the phase transition in the behavior of an open quantum walk on the integer lattice by analyzing its moments, revealing a transition between diffusive and ballistic spreading.

Contribution

It introduces a parameterized model of open quantum walks and characterizes the phase transition between diffusive and ballistic regimes through moment analysis.

Findings

Identification of a phase transition in quantum walk behavior

Analysis of first and second moments to determine spreading type

Demonstration of diffusive versus ballistic regimes

Abstract

It has been discovered that open quantum walks diffusively distribute in space, since they were introduced in 2012. Indeed, some limit distributions have been demonstrated and most of them are described by Gaussian distributions. We operate an open quantum walk on $\mathbb{Z}=\left\{0, \pm 1, \pm 2,\ldots\right\}$ with parameterized operations in this paper, and study its 1st and 2nd moments so that we find its standard deviation. The standard deviation tells us whether the open quantum walker shows diffusive or ballistic behavior, which results in a phase transition of the walker.