We investigate secure quantum teleportation (SQT) of squeezed coherent states in the presence of a noisy Gaussian environment. Unlike most previous studies that consider coherent states as the input to be teleported, we take squeezed coherent states as the information carriers and analyse how the squeezing of the input state influences the performance and security of the teleportation protocol. The quantum channel is modelled by a two-mode squeezed vacuum state shared between Alice and Bob, which interacts with a common squeezed thermal reservoir. The security of teleportation is ensured by simultaneously satisfying two conditions: a teleportation fidelity exceeding the classical limit F>2/3 and the existence of two-way quantum steering of the resource state. Using the covariance matrix formalism and the Lindblad master equation for open quantum systems, we study the time evolution of teleportation fidelity and Gaussian steering under the combined effects of dissipation, temperature, and environmental squeezing. The results show that the squeezing of the input coherent state plays a significant role in modifying the robustness of secure quantum teleportation against environmental noise. In particular, for suitable parameter regimes, input-state squeezing can enhance the tolerance of the protocol to thermal fluctuations and de-coherence, extending the temporal range in which SQT is achievable. These findings highlight the importance of the choice of input states in continuous-variable quantum communication protocols and provide new insights for optimizing secure quantum teleportation in realistic noisy environments.
Rana et al. (Sun,) studied this question.