Three-intensity decoy-state method for measurement-device-independent quantum key distribution

Abstract

We study the measurement-device-independent quantum key distribution (MDI-QKD) in practice with limited resources, when there are only three different states in implementing the decoy-state method. We present a tighter explicit formula to estimate the lower bound of the yield of two-single-photon pulses sent by Alice and Bob. Moreover, we show that the bounding of this yield and phase flip error of single-photon pulse pairs can be further improved by using other constraints which can be solved by a simple and explicit program. Our methods here can significantly improve the key rate and the secure distance of MDI-QKD with only three intensities.