A Multi Affine Geometric Framework for Quantum Nonlocality. Unifying Berry Phases, Entanglement, and Coherence

Abstract

We relate Berry-phase control and retained entropy geometry to recoverable coherence, entanglement, and Clauser-Horne-Shimony-Holt (CHSH) correlations. For a depolarized Bell pair subject to recorded phase noise, we determine exact CHSH optima when Bob retains his record and when he compresses it with his qubit into one qubit by any deterministic quantum channel. Some records preserve a violation that every such compression loses. The retained transverse metric gives sharp resource intervals. Nevertheless, for every finite derivative order, two finite readouts of the same noise can match all pulled-back monotone-metric and relative-entropy derivatives at faithful diagonal inputs while giving opposite recovered CHSH outcomes. Complete transverse entropy response determines the reliability law. A finite transitionless Berry loop realizes the channel; zero-expectation conditional control errors give a quadratic reduced-channel accuracy certificate. Transport, thermal, and accelerated-detector applications specialize established channel criteria under explicit preparation and accuracy assumptions. These model-dependent certificates supply neither a universal entanglement lifetime nor a detector-independent acceleration bound.