Bell's Theorem, Accountability and Nonlocality

TL;DR

This paper explores the implications of Bell's theorem by introducing the accountability hypothesis, demonstrating that explaining quantum correlations in individual runs leads to nonlocality and violations of parameter and outcome independence.

Contribution

It establishes that any detailed account of Bell experiment correlations must involve nonlocal influences, extending quantum theory and clarifying the nature of quantum nonlocality.

Findings

Any account of Bell correlations must violate parameter independence.

Quantum mechanics' outcome independence violation reflects nonlocality.

The accountability hypothesis constrains extensions of quantum theory.

Abstract

Bell's theorem is a fundamental theorem in physics concerning the incompatibility between some correlations predicted by quantum theory and a large class of physical theories. In this paper, we introduce the hypothesis of accountability, which demands that it is possible to explain the correlations of the data collected in many runs of a Bell experiment in terms of what happens in each single run. Under this assumption, and making use of a recent result by Colbeck and Renner [Nat. Commun. 2, 411 (2011)], we then show that any nontrivial account of these correlations in the form of an extension of quantum theory must violate parameter independence. Moreover, we analyze the violation of outcome independence of quantum mechanics and show that it is also a manifestation of nonlocality.