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Quantum key distribution(QKD) might be the most famous application of quantuminformation theory. The idea of QKD is not difficult to understand but inpractical implementations, many problems are needed to be solved, for example,the noise of the channels. Previous works usually discuss the estimate of thechannels and employ error-correcting procedures, whose feasibility andefficiency depend on the strength of the noise, or assist with entanglementdistillation procedures, which often result in a large consumption of stateswhile not all states can be distilled. This paper aims to study QKD over noisychannels including Pauli noises, amplitude damping noises, phase dampingnoises, collective noises as well as mixtures of them, in any strength withoutdistillations. We provide a method, called the testing state method, toimplement QKD protocols without errors over arbitrarily strength noisychannels. The method can be viewed as an error-correcting procedure, and canalso be employed for other tasks.

Quantum key distribution over noisy channels by the testing state method