Improved secure bounds for passive decoy state quantum key distribution system

The decoy-state method was proposed as an effective way to resist photon-number splitting attack in quantum key distribution (QKD) system. However, due to the limitation of computing power, the final key rate of the QKD system is affected by statistical fluctuation. Until now, the key rate of active decoy-state method under statistical fluctuations has been rigorously analysed and improved by applying the improved Chernoff bound. In this paper, the improved Chernoff bound method is applied in the passive decoy-state method and an improved bound for estimating the final key rate is obtained. The simulation results show that the maximum secure transmission distance by our method can reach 205 km under standard optical fiber, which is very close to the asymptotic limit of 212 km. With a number of pulses up to 1013, our method can reach the highest final key rates among existing results, which can be considered as the best choice for QKD implementations with passive mudulation.