Quantum key distribution (QKD) is one of the most important subjects in quantum information theory. There are two kinds of QKD protocols, prepare-measure protocols and entanglement-based protocols. For long-distance communications in noisy environments, entanglement-based protocols might be more reliable since they could be assisted with distillation procedures to prevent from noises. In this paper, we study the entanglement-based QKD over certain noisy channels and present schemes against collective noises, including collective dephasing and collective rotation, Pauli noises, amplitude damping noises, phase damping noises and mixtures of them. We focus on how to implement QKD protocols over noisy channels as in noiseless ones without errors. We also analyze the efficiency of the schemes, demonstrating that they could be more efficient than the standard entanglement-based QKD scheme.
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