Equivalence of Local Dynamical Hidden-Variable Models to Static Bell Locality

TL;DR

This paper proves that local dynamical hidden-variable models are equivalent to static Bell models, showing that reproducing quantum correlations requires violating at least one of three key assumptions.

Contribution

It introduces a generalized framework and rigorously demonstrates the equivalence of dynamical and static local hidden-variable models under certain conditions.

Findings

Dynamical models satisfying parameter independence reduce to static Bell models.

Reproducing quantum correlations necessitates violating locality, measurement independence, or realism.

Provides a universal diagnostic tool for analyzing local hidden-variable models.

Abstract

Bell's theorem establishes a fundamental incompatibility between quantum mechanics and local realism. However, persistent physical intuition suggests that local dynamical evolution or measurement-induced disturbances of local hidden variables might bypass this constraint. We establish a generalized transition-kernel framework encompassing dynamical measurement processes and rigorously prove that any dynamical model satisfying ontological parameter independence is mathematically reducible to a static Bell model. We reveal a fundamental trichotomy: to reproduce quantum correlations, a hidden-variable model must violate either (i) strict locality (e.g., ontological parameter and outcome independence), (ii) measurement independence, or (iii) realism. Our results provide a universal diagnostic tool, demonstrating that nonlocal statistical correlations can never be synthesized by purely local dynamical complexity.