An intuitive expression for inseparability condition of a two-mode squeezed vacuum state in a thermal environment

Considering the propagation of a two-mode optical field that is initially in a squeezed vacuum state in a thermal environment, we obtain an intuitive expression for inseparability condition of the two-mode mixed state which is given in the coherent state representation. This condition shows that the two modes have quantum entanglement if and only if the coefficient of the correlation term between the two modes is larger than that of the off-diagonal term of each mode in the density matrix. We find that even if the quantum channel is dynamically coupled to the thermal environment, the fidelity for teleporting coherent states larger than 1/2 is still the criterion for quantum teleportation. We also show that the entanglement, squeezing and quantum teleportation conditions are always consistent with each other.