Continuous variable entanglement in open quantum dynamics

TL;DR

This paper studies how 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 analysis of entanglement dynamics for Gaussian states in open quantum systems using covariance matrices and Peres-Simon criterion.

Findings

Entanglement can persist, vanish suddenly, or revive depending on environmental temperature.

The degree of entanglement is quantified by the logarithmic negativity over time.

Different initial states exhibit distinct entanglement evolution patterns.

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 analyze also the time evolution of the logarithmic negativity, which characterizes the degree of entanglement of the quantum state.