Dynamics of quantum entanglement in Gaussian open systems

TL;DR

This paper studies how quantum entanglement evolves over time in a system of two harmonic oscillators interacting with a thermal environment, revealing phenomena like entanglement sudden death and revival.

Contribution

It provides a detailed description of entanglement dynamics in Gaussian open systems using covariance matrices and identifies conditions for entanglement preservation or decay.

Findings

Entanglement can persist or vanish depending on environmental temperature.

Phenomena of entanglement sudden death and revival are observed.

Asymptotic states of maximal entanglement are characterized.

Abstract

In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we give a description of the dynamics of entanglement for a system consisting of two uncoupled harmonic oscillators interacting with a thermal environment. Using Peres-Simon necessary and sufficient criterion for separability of two-mode Gaussian states, we describe the evolution of entanglement in terms of the covariance matrix for a Gaussian input state. For some values of the temperature of environment, the state keeps for all times its initial type: separable or entangled. In other cases, entanglement generation, entanglement sudden death or a repeated collapse and revival of entanglement take place. We determine the asymptotic Gaussian maximally entangled mixed states (GMEMS) and their corresponding asymptotic maximal logarithmic negativity.