Suppressing the Errors Due to Mode Mismatch for $M$-Ary PSK Quantum Receivers Using Photon-Number-Resolving Detector

An M-ary phase shift keying quantum receiver with photon-number-resolving detectors considering the mode mismatch between the signal and local oscillating fields is analyzed. Compared with the quantum receiver using ON-OFF detectors, the errors due to mode mismatch can be suppressed effectively using photon-number-resolving detectors, especially for larger signal mean photon numbers.