The Uncertainty Principle as a Deficiency Bound: A Deficiency-Theoretic Perspective on Quantum Incompatibility

The uncertainty principle is traditionally viewed as a statement about the epistemic limits of observers or the intrinsic stochasticity of quantum states. We propose an operational reformulation in terms of experimental deficiency: the Robertson--Schr\"odinger inequality () ²/4 yields a lower bound on the Le Cam deficiency between incompatible experiments and any joint simulation. In the Gaussian (LAN) regime, this implies that every joint experiment attempting to simulate both position and momentum must incur strictly positive deficiency, with the Planck constant setting the information-loss scale. We introduce the saturation ratio = (²/4) / () as a dimensionless diagnostic of experimental optimality, and interpret decoherence as deficiency inflation via increased effective covariance. The framework applies to covariant Gaussian joint measurements (e. g. , Arthurs--Kelly-type schemes) and connects quantum uncertainty with classical statistical inference, identifying Gaussian measurements as deficiency-optimal. The resulting quantum--classical ``continuum'' claim is strictly operational: an ordering by saturation loss, not a metaphysical thesis of structural continuity, theory reduction, or ontological continuity.