Fidelity of quantum teleportation through noisy channels

Abstract

We investigate quantum teleportation through noisy quantum channels by solving analytically and numerically a master equation in the Lindblad form. We calculate the fidelity as a function of decoherence rates and angles of a state to be teleported. It is found that the average fidelity and the range of states to be accurately teleported depend on types of noises acting on quantum channels. If the quantum channels are subject to isotropic noise, the average fidelity decays to 1/2, which is smaller than the best possible value of 2/3 obtained only by the classical communication. On the other hand, if the noisy quantum channel is modeled by a single Lindblad operator, the average fidelity is always greater than 2/3. Quantum teleportation ͓1,2͔ is a process by which a sender, called Alice, transmits an unknown quantum state to a remote recipient, called Bob, via dual classical and quantum channels. Here a pair of maximally entangled particles, forming a quantum channel, should be used for the perfect quantum teleportation. However, while being distributed and kept by Alice and Bob, an entangled state may lose its coherence and become a mixed state due to the interaction with its environment.Bennett et al. ͓1͔ noted that the quantum channel that is less entangled reduces the fidelity of teleportation, and/or the range of states that can be accurately teleported. Popescu ͓3͔ investigated the relations among teleportation, Bell's inequalities, and nonlocality. It was demonstrated that there are mixed states that do not violate any Bell-type inequality, but still can be used for teleportation. Horodecki et al. ͓4͔ showed that any two mixed spin-1 2 states that violate the Bell-CHSH inequality are useful for teleportation. Also Horodecki et al. ͓6͔ proved the relation between the optimal fidelity of teleportation and the maximal singlet fraction of the quantum channel. Banaszek ͓7͔ investigated the fidelity of quantum teleportation using nonmaximally entangled states. Ishizaka ͓8͔ studied the quantum channel subject to local interaction with two-level environment. Although the studies cited above reveal the important relations between the degree of entanglement of the quantum channel and quantum teleportation, there seem to be little studies on the direct connection between the quantum teleportation and decoherence rates. Thus it might be interesting to know how the type and strength of noise acting on quantum channels affect the fidelity of quantum teleportation.In this paper, we investigate quantum teleportation through noisy channels by solving analytically and numerically a master equation in the Lindblad form. We obtain the fidelity of quantum teleportation as a function of decoherence time and angles of an unknown state to be teleported. Thus we explicitly demonstrate Bennett et al.'s argument that noisy quantum channels reduce the range of states to be accurately teleported. We also examine the characteristic dependence of the average fidelity on types of noises acting on qubits at each stage of the teleportatio...

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