Positivity in the presence of initial system-environment correlation

TL;DR

This paper investigates how initial correlations between a quantum system and its environment affect the positivity of dynamical maps, revealing conditions under which these maps remain positive or become nonpositive.

Contribution

It introduces a framework using assignment maps to analyze the conditions for positivity and complete positivity in the presence of initial system-environment correlations.

Findings

Initial correlations make the assignment map nonpositive.

Positivity depends on the interplay between the assignment map and system-environment coupling.

The role of this interplay in Markovian models is discussed.

Abstract

The constraints imposed by the initial system-environment correlation can lead to nonpositive Dynamical maps. We find the conditions for positivity and complete positivity of such dynamical maps by using the concept of an assignment map. Any initial system-environment correlations make the assignment map nonpositive, while the positivity of the dynamical map depends on the interplay between the assignment map and the system-environment coupling. We show how this interplay can reveal or hide the nonpositivity of the assignment map. We discuss the role of this interplay in Markovian models.