Homodyne-like detection for coherent state-discrimination in the presence of phase noise

We propose a homodyne-like detection scheme involving photon-number-resolving detectors to discriminate between two coherent states affected by either uniform or gaussian phase noise. A proof-of-principle experiment is performed employing two hybrid photodetectors, whose outputs are used in post processing to calculate the shot-by-shot photon-number differences. The performance of the strategy is quantified in terms of the error probability in discriminating the noisy coherent signals as a function of the characteristic noise parameters.