Entanglement in two-mode continuous variable open quantum systems

TL;DR

This paper analyzes how entanglement evolves in two-mode continuous-variable open quantum systems interacting with a thermal environment, revealing conditions for entanglement decay and asymptotic separability.

Contribution

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

Findings

Entanglement persists only at zero temperature for initial entangled states.

All states become separable asymptotically regardless of initial entanglement.

Initial separable states remain separable throughout evolution.

Abstract

In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we give a description of the continuous-variable entanglement for a system consisting of two noninteracting modes embedded in a thermal environment. By using the 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 Gaussian input states. For all values of the temperature of the thermal reservoir, an initial separable Gaussian state remains separable for all times. In the case of an entangled initial Gaussian state, entanglement suppression (entanglement sudden death) takes place, for non-zero temperatures of the environment. Only for a zero temperature of the thermal bath the initial entangled state remains entangled for finite times. We also show that, independent of its type - separable or entangled, the initial state evolves asymptotically to an equilibrium state which is always separable.