  Quantum teleportation of a continuous-variable state is studied for the
quantum channel of a two-mode squeezed vacuum influenced by a thermal
environment. Each mode of the squeezed vacuum is assumed to undergo the same
thermal influence. It is found that when the mixed two-mode squeezed vacuum for
the quantum channel is separable, any nonclassical features, which may be
imposed in an original unknown state, cannot be transferred to a receiving
station. A two-mode Gaussian state, one of which is a mixed two-mode squeezed
vacuum, is separable if and only if a positive well-defined $P$ function can be
assigned to it. The fidelity of teleportation is considered in terms of the
noise factor given by the imperfect channel. It is found that quantum
teleportation may give more noise than direct transmission of a field under the
thermal environment, which is due to the fragile nature of quantum entanglement
of the quantum channel.
