Inverse-Squeezing Kennedy Receiver for Near-Helstrom Discrimination of Displaced-Squeezed BPSK

Abstract: To address the discrimination problem of binary phase-shift keyed displaced squeezed vacuum states (S-BPSK), this paper proposes an Inverse-squeezing Kennedy (IS-Kennedy) receiver. This architecture incorporates an inverse-squeezing operator following the displacement operation of a conventional Kennedy receiver, mapping the S-BPSK signals onto equivalent large-amplitude coherent states. Furthermore, it employs a photon-number-resolving (PNR) detector to perform maximum a posteriori (MAP) decision-making. Theoretical analysis demonstrates that, under ideal conditions, the IS-Kennedy receiver effectively translates the transmitter's squeezing resources into a displacement gain at the receiver. Consequently, its error probability approaches the Helstrom bound across the entire energy spectrum, remaining within a constant factor of 3 dB. In the low-photon-number regime ($N \approx 0.6$), the proposed scheme surpasses the coherent-state limit, achieving an error rate below 1\%. Furthermore, this paper provides an in-depth analysis of system performance under non-ideal conditions, revealing the robustness of PNR detection against background dark counts and a characteristic ``parity photon-number step'' saturation effect arising from squeezing parameter mismatch.