Optimal state pairs for non-Markovian quantum dynamics

TL;DR

This paper investigates a measure of quantum non-Markovianity based on information exchange, proving that optimal state pairs for maximal memory effects are orthogonal, boundary states, which can be mixed, highlighting the nature of quantum memory effects.

Contribution

It provides a rigorous proof that optimal initial states for non-Markovianity measures are orthogonal boundary states, expanding understanding of quantum memory effects and their state dependencies.

Findings

Optimal state pairs must be orthogonal and on the boundary of physical states.

Quantum memory effects are maximal for initially distinguishable states.

Optimal states can be mixed, not necessarily pure.

Abstract

We study a recently proposed measure for the quantification of quantum non-Markovianity in the dynamics of open systems which is based on the exchange of information between the open system and its environment. This measure relates the degree of memory effects to certain optimal initial state pairs featuring a maximal flow of information from the environment back to the open system. We rigorously prove that the states of these optimal pairs must lie on the boundary of the space of physical states and that they must be orthogonal. This implies that quantum memory effects are maximal for states which are initially distinguishable with certainty, having a maximal information content. Moreover, we construct an explicit example which demonstrates that optimal quantum states need not be pure states.