General Theory of Decoy-State Quantum Cryptography with Dark Count Rate Fluctuation

The existing theory of decoy-state quantum cryptography assumes that the dark count rate is a constant, but in practice there exists fluctuation. We develop a new scheme of the decoy state, achieve a more practical key generation rate in the presence of fluctuation of the dark count rate, and compare the result with the result of the decoy-state without fluctuation. It is found that the key generation rate and maximal secure distance will be decreased under the influence of the fluctuation of the dark count rate.