Context-independent mapping and free choice are equivalent

TL;DR

This paper proves that in hidden variable models, the assumptions of free choice and context-independent mapping are logically equivalent, unifying two key concepts in the foundations of quantum mechanics.

Contribution

It establishes the complete generality of the equivalence between free choice and context-independent mapping assumptions in hidden variable models.

Findings

Proves the equivalence of free choice and CI mapping assumptions in all hidden variable models.

Shows that denying one assumption implies denying the other in empirical scenarios.

Clarifies the foundational relationship between local causality and contextuality in quantum theory.

Abstract

Free choice (or statistical independence) assumption in a hidden variable model (HVM) means that the settings chosen by experimenters do not depend on the values of the hidden variable. The assumption of context-independent (CI) mapping in an HVM means that the results of a measurement do not depend on settings for other measurements. If the measurements are spacelike separated, this assumption is known as local causality. Both free choice and CI mapping assumptions are considered necessary for derivation of the Bell-type criteria of contextuality/nonlocality. It is known, however, for a variety of special cases, that the two assumptions are not logically independent. We show here, in complete generality, for any system of random variables with or without disturbance/signaling, that an HVM that postulates CI mapping is equivalent to an HVM that postulates free choice. If one denies the possibility that a given empirical scenario can be described by an HVM in which measurements depend on other measurements' settings, free choice violations should be denied too, and vice versa. KEYWORDS: Contextuality; context-independent mapping; free choice; local causality; nonlocality.