Asymptotic entanglement in open quantum systems

TL;DR

This paper analyzes the long-term behavior of entanglement in two harmonic oscillators interacting with an environment, showing conditions under which they evolve into entangled or separable states.

Contribution

It provides a detailed description of asymptotic entanglement in open quantum systems using covariance matrices and the Peres--Simon criterion for Gaussian states.

Findings

Certain environments lead to asymptotic entangled states.

Other environments result in separable asymptotic states.

Logarithmic negativity quantifies the degree of entanglement.

Abstract

In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we solve in the asymptotic long-time regime the master equation for two independent harmonic oscillators interacting with an environment. We give a description of the continuous-variable asymptotic entanglement in terms of the covariance matrix of the considered subsystem for an arbitrary Gaussian input state. Using Peres--Simon necessary and sufficient condition for separability of two-mode Gaussian states, we show that for certain classes of environments the initial state evolves asymptotically to an entangled equilibrium bipartite state, while for other values of the coefficients describing the environment, the asymptotic state is separable. We calculate also the logarithmic negativity characterizing the degree of entanglement of the asymptotic state.