Time Evolution of Continuous Variable Entanglement in Open Quantum Systems

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 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 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.