Evaluation of photon number distribution for security certification of decoy quantum key distribution

Decoy-state quantum key distribution (QKD) requires information about the photon number distribution of the light sources. The photon number distribution of weak coherent photon sources has been assumed to follow a Poisson distribution. However, it is not yet clear whether picosecond laser pulses, used in high-speed QKD systems, satisfy this assumption due to the significant and rapid changes in carrier density and photon density in the laser cavity. It is necessary to establish a method to experimentally evaluate the photon number distribution of laser pulses with a duration of less than 100 ps. We have implemented three methods to identify a suitable approach for evaluating light sources in quantum key distribution systems. Our findings indicate that all three methods conclude that the photon numbers of the gain-switching laser pulse are consistent with a Poisson distribution. We then compared these methods based on their accuracy of photon number probability and ease of implementation. These considerations will establish a method suitable for the security certification of high-speed quantum key distributed devices.