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Decoy state method quantum key distribution (QKD) is one of the promisingpractical solutions to BB84 QKD with coherent light pulses. In the real world,however, statistical fluctuations with the finite code length cannot benegligible, and the securities of theoretical and experimental researches ofthe decoy method state QKD so far are based on the asymptotic GLLP's formulawhich guarantees only that the limit of eavesdropper's information becomes zeroas the code length approaches infinity. In this paper, we propose asubstantially improved decoy state QKD in the framework of the finite codelength and derive the upper bound of eavesdropper's information in the finitecode length decoy state QKD with arbitrary number of decoy states of differentintensities incorporating the finite statistics. We also show the performanceof our decoy QKD and optimal values of parameters by numerical simulation.

Security analysis of decoy state quantum key distribution incorporating finite statistics