Measurement device-independent quantum key distribution with heralded pair coherent state

The original measurement device-independent quantum key distribution is reviewed, and a modified protocol using heralded pair coherent state (HPCS) is proposed to overcome the quantum bit error rate associated with the dark count rate of the detectors in long-distance quantum key distribution. Our simulation indicates that the secure transmission distance can be improved evidently with HPCS owing to the lower probability of vacuum events when compared with weak coherent source scenario, while the secure key rate can be increased with HPCS due to the higher probability of single-photon events when compared with heralded single-photon source scenario. Furthermore, we apply the finite key analysis to the decoy state MDI-QKD with HPCS and obtain a practical key rate.