Two-mode squeezed vacuum state coupled to the common thermal reservoir

Entangled states play a crucial role in quantum information protocols, thus the dynamical behaviour of entanglement is of great importance. In this letter, we consider a two-mode squeezed vacuum state coupled to one thermal reservoir as a model of an entangled state embedded in an environment. As a criterion for entanglement we use a continuous-variable equivalent of the Peres–Horodecki criterion, namely the Simon criterion. To quantify entanglement we use the logarithmic negativity. We derive a condition, which assures that the state remains entangled in spite of the interaction with the reservoir. Moreover for the case of interaction with vacuum as an environment we show that a state of interest after infinitely long interaction is not only entangled, but also pure. For comparison we also consider a model in which each mode is coupled to its own reservoir.