Homogeneous Open Quantum Random Walks on a lattice

TL;DR

This paper investigates homogeneous open quantum random walks on a lattice, establishing limit theorems and ergodic properties for the position and state processes, with detailed analysis for two-dimensional internal spaces.

Contribution

It provides the first comprehensive analysis of translation-invariant OQRWs on lattices, including CLT, large deviations, and ergodic results for the position and state processes.

Findings

Established a central limit theorem for the position process.

Proved a large deviation principle for the position process.

Demonstrated ergodicity of the internal state process.

Abstract

We study Open Quantum Random Walks for which the underlying graph is a lattice, and the generators of the walk are translation-invariant. We consider the quantum trajectory associated with the OQRW, which is described by a position process and a state process. We obtain a central limit theorem and a large deviation principle for the position process, and an ergodic result for the state process. We study in detail the case of homogeneous OQRWs on a lattice, with internal space $h={\mathbb C}^2$.