Unification of witnessing initial system-environment correlations and witnessing non-Markovianity

TL;DR

This paper establishes a theoretical link between witnesses for initial system-environment correlations and non-Markovianity in open quantum systems, revealing how initial correlations influence non-Markovian behavior.

Contribution

It unifies the understanding of witnessing initial correlations and non-Markovianity, showing that the former bounds the latter through the role of state preparation.

Findings

Witness of initial correlations is an upper bound to non-Markovianity witness.

State preparation affects the detection of non-Markovian behavior.

Connections between initial correlations and non-Markovianity are clarified.

Abstract

We show the connection between a witness that detects dynamical maps with initial system-environment correlations and a witness that detects non-Markovian open quantum systems. Our analysis is based on studying the role that state preparation plays in witnessing violations of contractivity of open quantum system dynamics. Contractivity is a property of some quantum processes where the trace distance of density matrices decrease with time. From this, we show how a witness of initial-correlations is an upper bound to a witness of non-Markovianity. We discuss how this relationship shows further connections between initial system-environment correlations and non-Markovianity at an instance of time in open quantum systems.