Beyond Bell's Theorem: Correlation Scenarios

TL;DR

This paper explores correlation scenarios with multiple sources and no measurement choices, extending Bell's Theorem to identify nonlocal quantum correlations beyond traditional Bell scenarios.

Contribution

It introduces correlation scenarios as a generalization of Bell scenarios, demonstrating quantum nonlocality in new contexts and highlighting open problems in the field.

Findings

Quantum nonlocality observed in novel correlation scenarios

Bell's Theorem extended to scenarios with multiple sources

Many correlation scenarios do not originate from Bell scenarios

Abstract

Bell's Theorem witnesses that the predictions of quantum theory cannot be reproduced by theories of local hidden variables in which observers can choose their measurements independently of the source. Working out an idea of Branciard, Rosset, Gisin and Pironio, we consider scenarios which feature several sources, but no choice of measurement for the observers. Every Bell scenario can be mapped into such a \emph{correlation scenario}, and Bell's Theorem then discards those local hidden variable theories in which the sources are independent. However, most correlation scenarios do not arise from Bell scenarios, and we describe examples of (quantum) nonlocality in some of these scenarios, while posing many open problems along the way. Some of our scenarios have been considered before by mathematicians in the context of causal inference.