The Beta-Bound: Drift constraints for Gated Quantum Probabilities

arXiv:2601.22188v1 Announce Type: new
Abstract: Quantum mechanics provides extraordinarily accurate probabilistic predictions, yet the framework remains silent on what distinguishes quantum systems from definite measurement outcomes. This paper develops a measurement-theoretic framework for projective gating. The central object is the $beta$-bound, an inequality that controls how much probability assignments can drift when gating and measurement fail to commute. For a density operator $rho$, projector $F$, and effect $E$, with gate-passage probability $s = {rm Tr}(rho F)$ and commutator norm $varepsilon = |[F, E]|$, the symmetric partial-gating drift satisfies $|Delta p_F(E)| leq 2 sqrt{(1 – s)/s} cdot varepsilon$. The constant 2 is sharp. We introduce two diagnostic quantities: the coherence witness $W(rho, F) = |F rho (I – F)|_1$, measuring cross-boundary coherence, and the record fidelity gap $Delta_T(rho_F, R)$, measuring expectation-value change under symmetrisation. Three experimental vignettes demonstrate falsifiability: Hong–Ou–Mandel interferometry, atomic energy-basis dephasing, and decoherence-induced classicality. The framework is operational and interpretation-neutral, compatible with Everettian, Bohmian, QBist, and collapse approaches. It provides quantitative structure that any interpretation must accommodate, along with a template for experimental tests.