New formula for calculating the fidelity of teleportation and its applications

Abstract

Quantum teleportation plays an important role in quantum information science. In order to obtain the effect of quantum teleportation of a quantum state by using an entangled resource, the fidelity of teleporting the quantum state should be calculated. Braunstein and Kimble[Phys. Rev. Lett. 80 869 (1998)] derived a formula of calculating the fidelity of quantum teleportation for Gaussian entangled resource and any input state to be teleported. Then, the point is how to calculate the quantum teleportation fidelity for any entangled resource. In this paper, werealize this purpose by using the entangled state representation. First, we derive the Weyl expansion of any density operator by using the completeness relation between coherent state and P-representation. Then using the orthogonal property of entangled state representation and the traditional Kimble-Braunstein scheme of quantum teleportation, we further derive the mean density operator of the output state, which means that we establish the relation between the output density operator and the characteristic functions of the input state to be teleported and the entangled resources. The characteristic function of the output state is also derived which is in the concise form relating these two characteristic functions above. Then we further obtain a new formula for calculating the quantum teleportation fidelity for the coherent state input and any two-mode entangled resource. It is shown that the fidelity of teleportation can be easily calculated when the Q-function of the normally ordering form of entangled resource is known. This is a convenient way of obtaining the fidelity of teleportation. As its applications, some Gaussian and non-Gaussian entangled states are examined to teleport the coherent state, whose results are correct.