Continuous variable entanglement swapping in a thermal environment

With the application of a Wigner function description of a two-mode squeezed state, we study a protocol of continuous variable entanglement swapping in a noisy quantum channel. Assuming that the two initial entangled states are coupled with the same environment, we analyse the quantum state emerging from the swapping and obtain the inseparable condition for the output correlation. It is found that there is more noise resulting from the entanglement swapping than from the direct transmission, no matter what values of displacement gain are chosen.