Continuous variable quantum teleportation of a thermal state in a thermal environment

Abstract

The analytical formula for the fidelity of teleportation from Alice to Bob of a thermal state used as an input state is derived using the characteristic function approach. As a resource state it is used a continuous-variable two-mode bosonic state shared between Alice and Bob and the system is placed in a contact with a general environment. The quantum fidelity depends on the average thermal photon number of the input sate and on the parameters of the resource state and environment. In order to evaluate the parameters required for a successful quantum teleportation of a thermal state we estimate the evolution of the entanglement and fidelity of teleportation in the case when Alice and Bob share an initial squeezed thermal state in contact with a thermal bath. We work in the framework of the theory of open quantum systems based on completely positive dynamical semigroups and we use the Gorini–Kossakowski–Lindblad–Sudarshan master equation in order to describe the evolution of the system. The conditions for a successful quantum teleportation are the fidelity of teleportation larger than the threshold value of the classical fidelity of teleportation and entanglement present in the resource state. In order to assure the fulfillment of these conditions it is necessary to select the time of teleportation and to adjust the parameters characterizing the system (squeezing between the modes of the resource state, their average numbers of thermal photons and frequencies), and the temperature of the thermal reservoir. It is shown that in similar physical conditions, the fidelity of teleportation of the thermal states is larger than that one for a coherent state.