Analysis of quantum bit error rate based on single-photon source with Poisson distribution

Highly attenuated laser pulses with Poisson distribution are used as single-photon sources and the BB84 and B92 protocols are used for free-space quantum key distribution. By introducing the quantum channel transmission, the single-photon acquisition probability, the measuring factor and the sifting factor, the theoretical model of the quantum bit error rate was established and the expressions of the quantum bit error rate were given. The main factors that cause the quantum bit error rate are the optical elements, the detector dark noise and the space optical environment and these factors were analyzed. The quantum bit error rate was analyzed in the numerical simulation for the laser links between a ground station and a satellite in a low earth orbit. The results show that it is feasible to implement quantum key distribution between a ground station and a satellite in a low earth orbit and that it is the detector dark noise and the space optical environment that limit the link distance for free-space quantum key distribution.