Hybrid near-optimum binary receiver with realistic photon-number-resolving detectors

We propose a near-optimum receiver for the discrimination of binary phase-shift-keyed coherent states employing photon-number-resolving detectors. The receiver exploits a discrimination strategy based on both so-called homodyne-like and direct detection, thus resulting in a hybrid scheme. We analyze the performance and robustness of the proposed scheme under realistic conditions, namely, in the presence of inefficient detection and dark counts. We show that the present hybrid setup is near- optimum and beats both the standard quantum limit and the performance of the Kennedy receiver.