Finite-Key Analyses For Quantum Key Distribution Protocols

Constrained by the communication duration and the storage capacity, the number of exchanged pulses between the two parties is always finite, so the finite-key security analyses of quantum key distribution (QKD) protocols are of crucial importance in quantum communication.In practical quantum communication, the security of QKD protocols is influenced by imperfectness of devices. Based on the practical apparatuses, we analyzed the finite-key securities of QKD protocols under the three kinds of restrictions, as follows:For imperfect single-photon sources, we established a mathematical model for the phase randomized weak coherent decoy QKD protocol with finite number of pulses, and transformed the security analysis into a secure-key-rate problem. Considering the influence of the finite pulses on the statistics of the parameters, we designed an optimizing problem with the minimum of the final key rate as the objective function, solved the problem, and obtained the lower bounds of the final key rate and the secure distance for the finite standard BB84protocol, which improve the practical implementation of QKD protocols.Avoiding the information leakages in Plug&Play system involved in the implementation of decoy QKD protocols, we compared the finite-key rates of passive decoy QKD protocols under two different kinds of sources, i.e., parametric down-convention (PDC) source and weak coherent source, discussed the influences of intensity fluctuation on the final key rates, and concluded that the PDC source is more robust and more suitable for the practical QKD protocols.Against the side-channel attacks on the measurement devices, we analyzed the finite security of measurement-device-independent (MDI) QKD protocol, and summarized the relationship between the number of pulses and the secure key rate (the secure distance). With some reasonable values of experimental parameters, we also simulated the results of secure key rates as the function of transmission distances with some typical lengths of pulses.