Afterpulse analysis for passive decoy quantum key distribution

Abstract

The passive decoy method, a candidate for high-speed quantum key distribution (QKD), can prepare laser pulses with various photon-number distributions according to the responses of the transmitter's detectors, which usually adopts the single-photon avalanche photodiode (SPAD) in QKD. As an intrinsic characteristic of the SPAD, the afterpulse can introduce random detector responses, however, is regrettably ignored in passive schemes. Here we develop an analytical model for passive schemes in the finite-resource regime to describe the afterpulse effect on the detectors of both transmitter and receiver. The photon-number distributions biased by afterpulses are corrected, which reveals that the secure key rate is significantly overrated when the afterpulse is ignored. Moreover, our model can increase the tolerance of passive decoy source to afterpulse effect as the result shows that the secret key rates are comparable at different afterpulse probability by reoptimization.