Phase matching quantum key distribution is a promising scheme for remote quantum key distribution, breaking through the traditional linear key-rate bound. In practical applications, finite data size can cause significant system performance deterioration when data size is below 1010. In this paper, an improved statistical fluctuation analysis method is applied for the first time to two decoy-states phase matching quantum key distribution, offering new insights and potential solutions for improving the key generation rate and the maximum transmission distance while maintaining security. Moreover, we also compares the impacts of the proposed improved statistical fluctuation analysis method to those of the Gaussian approximation and Chernoff-Hoeffding boundary methods on system performance. The simulation results show that the proposed scheme significantly improves key generation rate and maximum transmission distance compared to the Chernoff-Hoeffding approach, and approaches the results obtained when the Gaussian approximation is employed. At the same time, the proposed scheme retains the same security level as the Chernoff-Hoeffding method, and is even more secure than the Gaussian approximation.

In this paper, a passive decoy state phase matching quantum key distribution scheme is proposed based on the heralded pair coherent state light source to make the protocol more practical and safe. Without changing the intensity of the light source, we can derive four different data sets by dividing the raw key data into four groups according to the combined results of detectors in source end. The scheme can make use of the different data sets to estimate the parameters and extract the secret key. The key generation rate formula is derived after the parameter estimation. The performance of the proposed scheme is analyzed with and without taking statistical fluctuation into consideration. The simulation results show that compared with the existing active decoy-state method, the proposed passive method has slightly lower key rate when the transmission distance is short, and has obviously higher key rate when the transmission distance exceeds 406[Formula: see text]km. The maximum safety transmission distance of the proposed scheme is 452[Formula: see text]km which is relatively further. According to the influence of statistical fluctuation, the performance of the proposed scheme declines as the length of the data falls. Even though the data size is [Formula: see text], the max safety transmission distance is also more than 400[Formula: see text]km.

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