Bell inequalities for the simplest exclusivity graph

TL;DR

This paper identifies the simplest bipartite Bell inequalities with quantum violations linked to the basic exclusivity graph, experimentally verifying their violations with entangled photons and addressing loopholes present in previous tests.

Contribution

It characterizes the most elementary logical Bell inequalities associated with the simplest exclusivity graph and experimentally confirms their quantum violations without loopholes.

Findings

Identified three fundamental bipartite Bell inequalities with quantum violations.

Experimentally observed violations consistent with quantum predictions.

Addressed the compatibility loophole in noncontextuality tests.

Abstract

Which is the simplest logical structure for which there is quantum nonlocality? We show that there are only three bipartite Bell inequalities with quantum violation associated with the simplest graph of relationships of exclusivity with a quantum-classical gap. These are the most elementary logical Bell inequalities. We show that the quantum violation of some well-known Bell inequalities is related to them. We test the three Bell inequalities with pairs of polarization-entangled photons and report violations in good agreement with the quantum predictions. Unlike other experiments testing noncontextuality inequalities with pentagonal exclusivity, the ones reported here are free of the compatibility loophole.