Non-Markovian evolution: a quantum walk perspective

TL;DR

This paper investigates non-Markovian quantum evolution using quantum walks, introducing spectral techniques to distinguish internal and environmental effects, and analyzing quantum correlations during the quantum-classical transition.

Contribution

It presents a novel spectral method to disambiguate internal and environmental sources of non-Markovianity in quantum walks, and explores quantum correlations in non-Markovian noisy systems.

Findings

Spectral techniques effectively distinguish internal vs. environmental non-Markovian effects.

Quantum correlations vary during the quantum to classical transition under non-Markovian noise.

Analysis indicates potential applications in complex quantum system dynamics.

Abstract

Quantum non-Markovianity of a quantum noisy channel manifests typically as information backflow, characterized by the departure of the intermediate map from complete positivity, though we indicate certain noisy channels that don't exhibit this behavior. In complex systems, non-Markovianity becomes more involved on account of subsystem dynamics. Here we study various facets of non-Markovian evolution, in the context of coined quantum walks, with particular stress on disambiguating the internal vs. environmental contributions to non-Markovian backflow. For the above problem of disambiguation, we present a general power-spectral technique based on a distinguishability measure such as trace-distance or correlation measure such as mutual information. We also study various facets of quantum correlations in the transition from quantum to classical random walks, under the considered non-Markovian noise models. The potential for the application of this analysis to the quantum statistical dynamics of complex systems is indicated.