Phase-time-encoding MDI QKD tolerant to detector imperfections

Measurement-device-independent quantum key distribution (MDI QKD) allows to eliminate the single-photon detector (SPD) vulnerabilities, increase the communication distance limits, and construct a multiple users key distribution network. Nevertheless, detector imperfections are able to decrease the secret key rate and maximum distance by orders of magnitude. In this work we propose a model of large SPD’s dead time for the phase-time-encoding MDI QKD. We also propose a modified measurement device (Charlie) scheme with four detectors which is able to partially restore the sifted key loss caused by dead time.