Residual-squeezing mechanism of mismatch in inverse-squeezing Kennedy receivers

The discrimination of quantum states is fundamental to quantum information processing. Inverse-squeezing Kennedy (IS-Kennedy) receivers can outperform the coherent-state binary phase-shift-keyed Helstrom benchmark at the same energy by converting transmitter-side squeezing into an effective coherent-state separation gain, without violating the Helstrom bound for the squeezed-state alphabet. This work investigates how squeezing mismatch degrades this mechanism. We show that imperfect inverse squeezing transforms the ideally nulled output into a residually squeezed state, thereby altering the photon-number statistics before detection. This residual-squeezing picture reveals a strong physical asymmetry between squeezing-magnitude and squeezing-phase mismatches. Magnitude mismatch produces an energy-independent error floor in the high-signal-energy regime, whereas phase mismatch generates a residual-squeezing term that grows with signal energy. In the small-residual-squeezing regime, this leads to a polynomial growth of the leading error contribution and a rapid collapse of the standard quantum limit advantage. We also identify a parity-step effect in photon-number-resolving detection: Because the nulled residual squeezed vacuum contains only even photon numbers, increasing detector resolution improves the high-energy robustness only when the effective saturation threshold crosses the next even photon number. These results identify phase locking as the dominant bottleneck for IS-Kennedy-type non-Gaussian receivers under unitary squeezing mismatch and provide design guidelines for robust squeezed-state quantum receivers.