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

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.

31 pages, 5 figures

References in corpus (1)

• Non-Markovian generalization of the Lindblad theory of open quantum systems

Cited by in corpus (9)

• On a generalized Central Limit Theorem and Large Deviations for Homogeneous Open Quantum Walks
• Lazy Open Quantum Walks
• QSWalk.jl: Julia package for quantum stochastic walks analysis
• Central limit theorems for open quantum random walks on the crystal lattices
• Limit properties of global interaction stochastic quantum walks on directed graphs
• One-dimensional Continuous-Time Quantum Markov Chains: qubit probabilities and measures
• Site Recurrence for continuous-time open quantum walks on the line
• Quantum Markov processes on graphs, monitoring and hitting times
• Application of graph theory in quantum computer science