Calibration limited quantum advantage in dose constrained biomolecular absorption spectroscopy

Abstract Quantum optical probes can improve absorption measurements per specimen photon, but uncertain throughput can obscure the concentration advantage. We analyze two-wavelength concentration estimation with unknown common throughput, a local absorbed-photon budget and independently calibrated relative spectral response. For number-state and coherent probes, exact zero-background photon-counting Fisher bounds yield closed-form optimal exposure allocations. Finite spectral-calibration information introduces an additive concentration-variance floor. Consequently, the optimized fixed-dose variance advantage approaches unity as specimen exposure increases while calibration information remains fixed. We derive an explicit calibration requirement for a prescribed advantage and a joint allocation rule when sample exposure and calibration share an accounting budget. Unlabelled Poisson background is treated through an explicit likelihood and a separately identified first-order estimator approximation. Reproducible dimensionless calculations verify the analytical allocations and illustrate the calibration-limited regime. The contribution is a calibration-aware design criterion for linear biomolecular absorption assays, not a universal quantum limit or a clinical performance claim. The model applies to a known dominant absorber with a known path length and negligible scattering. It distinguishes improvements attainable through photon statistics from uncertainty that instead requires better spectral calibration.