Study on Statistical Analysis Method of Decoy-state Quantum Key Distribution with Finite-length Data

In order to solve the statistical fluctuation problem caused by the finite data length in the practical quantum key distribution system, four commonly used statistical methods, DeMoivre-Laplace theorem, Chebyshev inequality, Chernoff boundary and Hoeffding boundary, are used to analyze. The application conditions of each method are discussed, and the effects of data length and confidence level on quantum key distribution security performance are simulated and analyzed. The simulation results show that the applicable conditions of Chernoff boundary are most consistent with the reality of the practical quantum key distribution system with finite-length data. Under the same experimental conditions, the secure key generation rate and secure transmission distance obtained by Chernoff boundary are better than those of the other three methods. When the data length and confidence level change, the stability of the security performance obtained by the Chernoff boundary is the best.