Measure for the Degree of Non-Markovian Behavior of Quantum Processes in Open Systems

TL;DR

This paper introduces a general measure for quantifying non-Markovian behavior in open quantum systems based on trace distance, capturing information flow dynamics.

Contribution

It proposes a novel, general measure for non-Markovianity in quantum processes that links information flow to dynamical maps.

Findings

The measure is based on trace distance and quantifies distinguishability of quantum states.

It interprets non-Markovianity as information flow from environment to system.

The measure is nonzero when there is a backflow of information.

Abstract

We construct a general measure for the degree of non-Markovian behavior in open quantum systems. This measure is based on the trace distance which quantifies the distinguishability of quantum states. It represents a functional of the dynamical map describing the time evolution of physical states, and can be interpreted in terms of the information flow between the open system and its environment. The measure takes on nonzero values whenever there is a flow of information from the environment back to the open system, which is the key feature of non-Markovian dynamics.