Physics-regularized Chernoff-bound analysis of the quantum-illumination advantage through a plasma sheath

Abstract

We ask whether the quantum-illumination (QI) advantage survives the lossy, thermally bright plasma sheath enveloping hypersonic vehicles. Computing the quantum Chernoff bound exactly in truncated Fock space for both QI and equal-energy classical illumination through an identical Appleton-type sheath channel, we find the advantage holds near +3.1 dB across transparent-to-moderate electron densities, then collapses beyond the blackout threshold and ultimately inverts deeper in the blackout regime, where round-trip loss destroys the signal–idler correlations. A physics-regularized residual surrogate makes a Gaussian proxy for the exponent ξ tractable across the full parameter space (RMSE = 0.513 ± 0.008 in log₁₀ ξ; R² = 0.951; 16.7% median error, versus 21.0% for a plain network; five seeds), degrading to 57.8% under out-of-distribution blackout conditions. We characterize this Gaussian proxy against exact Fock-space values in the entangled regime and find it underestimates the exact exponent by a factor of 3.7 to 5.0, decreasing with background, while preserving correct parameter ordering — reported explicitly so the surrogate is read as approximating a validated proxy rather than the exact bound.