Suppressing the Errors due to Mode Mismatch for M-ary PSK Quantum Receivers by Photon-Number-Resolving Detector

A M-ary phase shift keying (PSK) quantum receiver consisting of displacement operations, photon counting, and electrical feed-back adaptive measurements is analyzed with a realistic model considering the effects of the sub-unity quantum efficiency and the dark counts of single-photon detectors, as well as the transmittance and the mode mismatch of beam splitters. Among these factors, the mode mismatch has the greatest impact on the error probability of the receiver with on-off detectors. The errors due to mode mismatch can be suppressed effectively by using photon-number-resolving detectors (PNRD) instead of on-off detectors.