  Quantum communication networks can be built on quantum teleportation, which
is the transmission of an unknown quantum state from a sending station to a
remote receiving station supported by entangled states and classical
communication. We use a continuous variable two-mode squeezed vacuum state as a
resource state for the quantum teleportation. This state is shared by Alice and
Bob, and their system comes into contact with a squeezed thermal environment.
The conditions for a secure quantum teleportation require a teleportation
fidelity larger than 2/3 and two-way steering of the resource state. We
investigate the time evolution of the steering and the fidelity of
teleportation in order to determine the values of the parameters required for a
successful secure quantum teleportation of a coherent Gaussian state. We show
that the temperature, dissipation rate and squeezing parameter of the squeezed
thermal reservoir limit the feasible duration for secure quantum teleportation,
while by increasing the squeezing parameter of the initial state one can
effectively expand the temporal range for a successful secure quantum
teleportation.
