Contextuality and correlation loopholes are equivalent

TL;DR

This paper demonstrates that contextual hidden variables can be traced back to initial data, showing that the correlation loophole in Bell tests remains unclosed, which impacts interpretations of quantum nonlocality.

Contribution

It establishes the equivalence between contextuality and correlation loopholes and introduces a method to backward-propagate hidden variables using Green's functions.

Findings

Bell inequality derivation depends on uncorrelated initial data.

The correlation loophole in Bell tests remains open.

Contextual hidden variables can be linked to initial conditions.

Abstract

We show that contextual hidden variables including the effect of the measuring devices can be backward-propagated by means of the Green's function to initial Cauchy hidden data. If this data is uncorrelated in spacelike-disjoint sets, the CHSH-Bell inequality can be derived. However, the correlation loophole remains unclosed.