Monogamy and backflow of mutual information in non-Markovian thermal baths

TL;DR

This paper explores how mutual information behaves in tripartite quantum systems with thermal baths, revealing conditions for monogamy, information flow reversibility, and non-Markovian dynamics.

Contribution

It proves monogamy properties of mutual information in tripartite states and analyzes information dynamics in non-Markovian thermal bath models.

Findings

Mutual information is monogamous in generic pure tripartite states.

Local information can convert into delocalized information over time.

Reversibility of information flow occurs at low temperatures in finite thermal baths.

Abstract

We investigate the dynamics of information among the parties of tripartite systems. We start by proving two results concerning the monogamy of mutual information. The first one states that mutual information is monogamous for generic tripartite pure states. The second shows that in general mutual information is monogamous only if the amount of genuine tripartite correlations is large enough. Then, we analyze the internal dynamics of tripartite systems whose parties do not exchange energy. In particular, we allow for one of the subsystems to play the role of a finite thermal bath. As a result, we find a typical scenario in which local information tends to be converted into delocalized information. Moreover, we show that (i) the information flow is reversible for finite thermal baths at low temperatures, (ii) monogamy of mutual information is respected throughout the dynamics, and (iii) genuine tripartite correlations are typically present. Finally, we analytically calculate a quantity capable of revealing favorable regimes for non-Markovianity in our model.