Heterodyne-like feedforward partitioned-displacement hybrid receiver for QPSK coherent state discrimination with realistic photon-number-resolving detectors

This paper proposes a hybrid receiver, the heterodyne-like feedforward partitioned-displacement hybrid (HFPH) receiver, for discriminating quadrature phase-shift keying (QPSK) coherent states using photon-number-resolving (PNR) detectors. The receiver integrates a heterodyne-like (HL) measurement scheme with a Shuro-like (SL) displacement backend, forming a feedforward architecture that dynamically adapts to real-time decisions. We theoretically analyze the performance of the proposed scheme under practical imperfections, including detection inefficiency, dark counts, and imperfect interference visibility. Our results demonstrate that the HFPH receiver can surpass the standard quantum limit under these non-ideal conditions and exhibits enhanced robustness compared to the benchmark receiver.