Reduced dynamical maps in the presence of initial correlations

TL;DR

This paper develops a framework for constructing completely positive dynamical maps in open quantum systems with initial correlations, including states with non-zero discord, highlighting non-uniqueness and relevance for quantum dynamics.

Contribution

It introduces a general method for constructing CP maps with initial correlations, extending previous approaches to include discordant states and analyzing non-uniqueness issues.

Findings

Framework accommodates initial correlations with non-zero discord.

Explicitly demonstrates non-uniqueness of CP extensions outside the compatibility domain.

Connects the new approach to existing literature on open quantum system dynamics.

Abstract

We introduce a general framework for the construction of completely positive dynamical evolutions in the presence of system-environment initial correlations. The construction relies upon commutativity of the compatibility domain obtained by considering the marginals with respect to the environmental degrees of freedom of the considered class of correlated states. Our approach allows to consider states whose discord is not necessarily zero and explicitly show the non-uniqueness of the completely positive extensions of the obtained dynamical map outside the compatibility domain. The relevance of such maps for the treatment of open quantum system dynamics is discussed and connection to previous literature is critically assessed.