Measurement-device-independent quantum key distribution with odd coherent state

Measurement-device-independent quantum key distribution (MDI-QKD) is immune to all the detection attacks, thus when it is combined with the decoy-state method, the final key rate can be obtained by estimating the gain and quantum bit error rate for various input photon numbers. In this paper, we propose to perform MDI-QKD with odd coherent state (OCS) and compare the results with weak coherent source scenario. Our simulation indicates that both the secure key rate and transmission distance can be improved evidently with OCS owing to the lower probability of multi-photon events of the OCS. Furthermore, we apply the finite key analysis to the decoy-state MDI-QKD with OCS and obtain a practical key rate.