Open Quantum Random Walks: reducibility, period, ergodic properties

TL;DR

This paper extends classical Markov chain concepts like irreducibility, period, and ergodicity to open quantum random walks, analyzing their structural and long-term behavior.

Contribution

It generalizes classical Markov chain properties to the quantum setting, providing new insights into the structure and ergodic behavior of open quantum random walks.

Findings

Recovered classical results for ergodic behavior

Decomposed quantum walks into irreducible subsystems

Characterized stationary states in quantum context

Abstract

We study the analogues of irreducibility, period, and communicating classes for open quantum random walks, as defined by Attal et al. (J. Stat. Phys., 2012). We recover results similar to the standard ones for Markov chains, in terms of ergodic behavior, decomposition into irreducible subsystems, and characterization of stationary states.