Near-optimal discrimination of displaced squeezed binary signals using displacement, inverse-squeezing, and photon-number-resolving detection

Abstract

We propose an inverse-squeezing Kennedy receiver for discriminating binary phase-shift-keyed displaced squeezed vacuum states. The receiver combines a Kennedy-type nulling displacement, an orthogonally oriented inverse-squeezing operation and photon-number-resolving detection with a maximum-a-posteriori threshold rule. Its key mechanism is that the inverse-squeezing stage converts transmitter-side squeezing into enhanced photon-number contrast, or equivalently an effective coherent-state separation gain, that can be directly exploited at the measurement stage. Under ideal equal-prior conditions, the receiver surpasses the standard quantum limit for squeezed-state binary phase-shift keying at approximately $N\approx 0.3$, outperforms the Helstrom bound of coherent-state binary phase-shift keying at approximately $N\approx 0.4$, and reaches the 1\% error level near $N\approx 0.6$. We further analyze its performance under realistic imperfections, including finite detector efficiency, dark counts, channel phase diffusion, receiver thermal noise and transmission loss. The results show that adaptive thresholding preserves robust performance against detector and noise imperfections over practical parameter ranges, whereas transmission loss progressively suppresses the squeezing-enabled advantage. These findings indicate that, for the fixed source parametrization adopted in this work, the proposed receiver is most advantageous in the low-loss regime, especially at low source energies.