Entanglement dynamics of two-mode Gaussian states in a thermal environment

Abstract

Within 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 uncoupled modes interacting with a thermal environment. Using the Peres–Simon necessary and sufficient criterion for separability of two-mode Gaussian states, we describe the generation and 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 periodic 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.