Central Limit Theorem and Large Deviation Principle for Continuous Time Open Quantum Walks

TL;DR

This paper studies continuous time open quantum walks (CTOQWs) on integer lattices, establishing a central limit theorem and large deviation principle for the walker's position, extending classical probabilistic results to quantum stochastic processes.

Contribution

It introduces a rigorous analysis of homogeneous CTOQWs, proving a central limit theorem and large deviation principle for their quantum trajectories, a novel extension of classical results to quantum walks.

Findings

Proved a Central Limit Theorem for the position of CTOQWs.

Established a Large Deviation Principle for quantum trajectories.

Extended classical probabilistic results to quantum stochastic processes.

Abstract

Open Quantum Walks (OQWs), originally introduced by S. Attal, are quantum generalizations of classical Markov chains. Recently, natural continuous time models of OQW have been developed by C. Pellegrini. These models, called Continuous Time Open Quantum Walks (CTOQWs), appear as natural continuous time limits of discrete time OQWs. In particular they are quantum extensions of continuous time Markov chains. This article is devoted to the study of homogeneous CTOQW on $\mathbb{Z}^d$. We focus namely on their associated quantum trajectories which allow us to prove a Central Limit Theorem for the "position" of the walker as well as a Large Deviation Principle.