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

Entanglement swapping of two-mode Gaussian states is investigated by use of quantum teleportation protocol of continuous variables. In the entanglement swapping protocol, we take the two-mode squeezed vacuum which is exposed in a thermal environment as a mixed-quantum-channel state and a two-mode standard form Gaussian state as an input state to be teleported. When the input state is pure, we find that the swapped state is inseparable if and only if both the input state and the quantum-channel state are entangled. When the input state is mixed and entangled, we find that the swapped state is inseparable only if the quantum-channel state is sufficiently much entangled. We also notice that the required minimum entanglement in the mixed quantum channel to maintain entanglement in the swapped state strongly depends on the global purity of the input state.