Evolution of entanglement of two-mode Gaussian states under a dissipative environment

The equivalence of mode squeezing and quantum entanglement for two-mode Gaussian states under a dissipative environment is discussed. The evolution of two-mode Gaussian states in a dissipative environment is considered in two different scenarios. In the first case, we squeeze the individual modes, evolve them under a dissipative environment and then entangle them using passive optics. In the second case, we squeeze the modes, entangle them using passive optics and then evolve them under a dissipative environment. The entanglement properties of the final state are compared in these two different cases. It is shown that under certain circumstances, the surviving entanglement is the same in both the cases.