Performance of passive decoy-state quantum key distribution with mismatched local detectors

In quantum key distribution (QKD), passive decoy-state method can simplify the intensity modulation and reduce some of side-channel information leakage and modulation errors. It is usually implemented with a heralded single-photon source. In [Physical Review A 96, 032312 (2016)], a novel passive decoy-state method is proposed by Wang et al., which uses two local detectors to generate more detection events for tightly estimating channel parameters. However, in original scheme, the two local detectors are assumed to be identical, including same detection efficiency and dark count rate, which is often not satisfied in realistic experiment. Therefore, in this paper, we construct a model for this passive decoy-state QKD scheme with two mismatched detectors and explore the effect on QKD performance with certain parameter. We also take the finite-size effect into consideration, showing the performance with statistical fluctuations. The results show that the efficiencies of local detectors affect the key rate more obviously than dark count rates. Our work provides a reference value for realistic QKD system.