Beating the standard quantum limit for binary phase-shift-keying discrimination with a realistic hybrid feed-forward receiver

We propose a hybrid feed-forward receiver (HFFRE) for the discrimination of binary phase-shift-keyed coherent states based on the appropriate combination of a displacement feed-forward receiver (DFFRE) and a homodynelike setup employing a low-intensity local oscillator and photon-number-resolving detectors. We investigate the performance of the proposed scheme, also addressing realistic scenarios in the presence of nonunit quantum detection efficiency, dark counts, and visibility reduction. The present HFFRE outperforms the DFFRE in all conditions, beating the standard quantum limit in particular regimes.