Secure Quantum Teleportation of Squeezed Thermal States

Quantum teleportation is a fundamental protocol in quantum information science. It represents a critical resource for quantum communication and distributed quantum computing. We derive an analytical expression of the fidelity of teleportation of an input squeezed thermal state using for teleportation a bipartite Gaussian resource state shared between Alice and Bob. Each mode of the resource state is susceptible to the influence of the environment. We employ the characteristic function approach in conjunction with the covariance matrix formalism. The fidelity of teleportation is expressed in terms of input and resource state covariance matrices. We investigate, as an example, the feasibility of secure quantum teleportation of a squeezed thermal state using a two-mode resource state whose modes are placed in separate thermal baths. A successful quantum teleportation requires meeting two criteria: the presence of two-way quantum steering and a teleportation fidelity exceeding the classical threshold. The quantum steering is by nature asymmetric and has found applications in quantum cryptography and secure quantum teleportation. Weak squeezing and a high number of average thermal photons in the input states lead to an increase in the fidelity of teleportation. Generally, steering disappears much faster than the fidelity of teleportation decreases below its classical limit.