We have studied the standard quantum teleportation of an arbitrary single qubit state for the situation in which a two-qubit X-state as a resource successively passes through correlated quantum channels, including amplitude-damping, phase-damping, and depolarizing channels. Analytical expressions of full entangled fraction (which is related to fidelity of quantum teleportation) suffered from these noisy channels are presented. The results demonstrate that there is a threshold value mu, above which the source state even subjected to decoherence becomes useful for quantum teleportation. Besides, we also develop an effective strategy to enhance quantum teleportation fidelity under decoherence channels by means of filtering operation. The underlying physical mechanism of the enhancement of fidelity is also analyzed.
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