Interaction-induced correlations and non-Markovianity of quantum dynamics

TL;DR

This paper explores how system-environment correlations influence non-Markovian behavior in quantum dynamics, providing bounds on trace distance increases and illustrating with relevant physical examples.

Contribution

It establishes a quantitative link between system-environment correlations and non-Markovianity, offering bounds on trace distance changes in open quantum systems.

Findings

Trace distance increase is bounded by system-environment correlations.

Non-Markovian behavior is linked to finite-time correlations.

Illustrated with a non-Markovian dephasing and spin chain examples.

Abstract

We investigate the conditions under which the trace distance between two different states of a given open system increases in time due to the interaction with an environment, therefore signalling non-Markovianity. We find that the finite-time difference in trace distance is bounded by two sharply defined quantities that are strictly linked to the occurrence of system-environment correlations created throughout their interaction and affecting the subsequent evolution of the system. This allows to shed light on the origin of non-Markovian behaviours in quantum dynamics. We best illustrate our findings by tackling two physically relevant examples: a non-Markovian dephasing mechanism that has been the focus of a recent experimental endeavour and the open-system dynamics experienced by a spin connected to a finite-size quantum spin chain.