Photon loss makes Gaussian boson sampling easier to simulate classically. A standard approach replaces the lossy input by classical light, and it stays accurate while the mean number of surviving photons grows no faster than the square root of the number
N of squeezed inputs at fixed squeezing and accuracy. We prove that this scale is a limit of replacement by classical light. For explicit interferometers, no state with a nonnegative Glauber--Sudarshan
P representation, Gaussian or not and however correlated, keeps the error in the photon count distribution small beyond this scale. We then surpass this limit by approximating the detection instead of the input. The sampler evolves the state exactly between detections and, after each detection, replaces the conditional state by a Gaussian with the same covariance. For every interferometer its total variation error is
O(Nη3) at polynomial expected cost, where
η is the photon survival probability. The mean surviving photon number can therefore grow as
N2/3 at fixed accuracy. A separate pair construction reaches
N3/4 when every input mode is equally squeezed.
Classical reaction dynamics suggests transport through an index-1 saddle is organized not just by flux, but by local symplectic width scales of bounded proxy neighborhoods near the bottleneck. We investigate if a related geometric effect appears in the quantum regime for highly squeezed Gaussian wavepackets. Building on de Gosson's symplectic approach, we analyze how transverse bath-mode squeezing modifies transmission across a quantum normal-form (QNF) bottleneck.
To avoid the instability of propagating states with extreme phase-space eccentricity, we use the Weyl-symbol formulation of the QNF. For the quadratic saddle-center model, we derive an exact baseline transmission formula by convolving the bath's squeezed-state number distribution with the 1D Kemble transmission factor. For anharmonic truncated QNF models, we enforce strict algebraic energy conservation and evaluate exact Gaussian expectation-value diagnostics of the Weyl symbol via Wick-Isserlis moment formulas.
Results reveal a pronounced squeeze-induced suppression of transmission. As the squeezed state's bath-plane geometric scale grows relative to the classical candidate width, the expected bath action grows rapidly. Consequently, effective reactive energy is strongly depleted, driving transmission into a severely suppressed regime. We interpret this as evidence of a quantum geometric suppression mechanism consistent with the classical candidate symplectic-width picture. While not yet a rigorous quantum non-squeezing theorem, this work provides a concrete framework linking squeezed-state covariance geometry, normal-form action scales, and mode-specific quantum reactivity near an index-1 saddle.