Non-Markovianity Quantifier of an Arbitrary Quantum Process

TL;DR

This paper introduces an analytical and computational approach to quantify non-Markovianity in quantum processes using entanglement measures, enabling easier experimental detection and analysis.

Contribution

It provides an analytical solution for the optimization problem in non-Markovianity quantification and proposes a computable measure based on generalized robustness of entanglement.

Findings

Analytical solution for entanglement-based non-Markovianity quantification.

A semidefinite programming method for calculating the measure.

Experimental witness for non-Markovianity via observable expectation values.

Abstract

Calculating the degree of non-Markovianity of a dissipative process is a difficult task, even for the dynamics of a single qubit, given the complex maximization problem. In this work, focusing on the entanglement-based quantifier of non-Markovianity, we present an analytical solution for such an optimization problem. We then propose a computable non-Markovianity measure based on generalized robustness of entanglement, an entanglement measure that can be readily calculated by a semidefinite programming method. We show that the non-Markovianity, in a given interval of time, can be witnessed by calculating the expectation value of an observable, making it attractive for experimental investigations.