Quantum non-Markovian environment-to-system backflows of information: non-operational vs. operational approaches

TL;DR

This paper compares non-operational and operational approaches to quantum non-Markovianity, analyzing how environment-to-system information backflows are interpreted and implemented in different models, with a focus on their differences and advantages.

Contribution

It provides a detailed comparison of non-operational and operational definitions of quantum non-Markovianity using diverse models and dynamics, highlighting their respective strengths and limitations.

Findings

Non-operational approach based on state distinguishability.

Operational approach based on measurement outcome correlations.

Analysis of a non-Markovian depolarizing map with environment dynamics.

Abstract

Quantum memory effects can be qualitatively understood as a consequence of an environment-to-system backflow of information. Here, we analyze and compare how this concept is interpreted and implemented in different approaches to quantum non-Markovianity. We study a non-operational approach, defined by the istinguishability between two system states characterized by different initial conditions, and an operational approach, which is defined by the correlation between different outcomes associated to successive measurement processes performed over the system of interest. The differences, limitations, and vantages of each approach are characterized in detail by considering diverse system-environment models and dynamics. As a specific example, we study a non-Markovian depolarizing map induced by the interaction of the system of interest with an environment characterized by incoherent and coherent self-dynamics.