Bell inequality and common causal explanation in algebraic quantum field theory

TL;DR

This paper investigates whether non-classical common causal explanations can justify Bell inequalities in algebraic quantum field theory, finding that such explanations exist even when Bell inequalities are violated, expanding the understanding of causality in quantum physics.

Contribution

It demonstrates that non-classical common causal explanations are possible for quantum correlations that violate Bell inequalities, unlike classical explanations.

Findings

Classical common causes cannot explain Bell inequality violations.

Non-classical common causes can explain correlations violating Bell inequalities.

The range of causal explanations in quantum theory is broader than classical constraints.

Abstract

Bell inequalities, understood as constraints between classical conditional probabilities, can be derived from a set of assumptions representing a common causal explanation of classical correlations. A similar derivation, however, is not known for Bell inequalities in algebraic quantum field theories establishing constraints for the expectation of specific linear combinations of projections in a quantum state. In the paper we address the question as to whether a 'common causal justification' of these non-classical Bell inequalities is possible. We will show that although the classical notion of common causal explanation can readily be generalized for the non-classical case, the Bell inequalities used in quantum theories cannot be derived from these non-classical common causes. Just the opposite is true: for a set of correlations there can be given a non-classical common causal explanation even if they violate the Bell inequalities. This shows that the range of common causal explanations in the non-classical case is wider than that restricted by the Bell inequalities.