Entropic witness for quantum memory in open system dynamics

TL;DR

This paper introduces a computationally simple entropic criterion to detect quantum memory in open quantum systems, applicable to both finite-dimensional and continuous-variable systems, facilitating analysis of non-Markovian dynamics.

Contribution

The authors propose a new von Neumann entropy-based witness for quantum memory that is easily computable for systems of any dimension, improving over previous methods.

Findings

Effective detection of quantum memory in finite-dimensional qudit systems.

Applicability of the criterion to continuous-variable quantum systems.

Analysis of non-Markovian Gaussian dynamics of a damped harmonic oscillator.

Abstract

The dynamics of open quantum system are often modeled by non-Markovian processes that account for memory effects arising from interactions with the environment. It is well-known that the memory provided by the environment can be classical or quantum in nature. Remarkably, the quantumness of the memory can be witnessed locally by measurements on the open system alone, without requiring access to the environment. However, existing witnesses are computationally challenging for systems beyond qubits. In this work, we present a tractable criterion for quantum memory based on the von Neumann entropy, which is easily computable for systems of any dimension. Using this witness, we investigate the nature of memory in a class of physically motivated finite-dimensional qudit dynamics. Moreover, we demonstrate that this criterion is also suitable for detecting quantum memory in continuous-variable systems. As an illustrative example, we analyze non-Markovian Gaussian dynamics of a damped harmonic oscillator.