Bell inequalities for the simplest exclusivity graph

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.

REVTeX4, 6 pages, 4 figures

References in corpus (5)

• A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations
• A simple test for hidden variables in spin-1 system
• Experimental non-classicality of an indivisible quantum system
• Experimental fully contextual correlations
• Experimental observation of impossible-to-beat quantum advantage on a hybrid photonic system

Cited by in corpus (23)

• Graph-Theoretic Approach to Quantum Correlations
• Local orthogonality as a multipartite principle for quantum correlations
• Kochen-Specker Contextuality
• The exclusivity principle forbids sets of correlations larger than the quantum set
• Basic exclusivity graphs in quantum correlations
• Exploring the Local Orthogonality Principle
• Multigraph approach to quantum non-locality
• Quantum Contextuality with Stabilizer States
• Semi-definite programming and quantum information
• Probing the limits of correlations in an indivisible quantum system
• Graph-theoretic strengths of contextuality
• Testing noncontextuality inequalities that are building blocks of quantum correlations
• Experimental test of high-dimensional quantum contextuality based on contextuality concentration
• Gleason, Kochen-Specker, and a competition that never was
• Quantum realism and quantum surrealism
• The Exclusivity Principle and the Set of Quantum Correlations
• Quantum sets of the multicolored-graph approach to contextuality
• A Logical Proof of Quantum Correlations Requiring Entanglement Measurements
• Graphical Framework for Non-Gaussian Quantum States
• Universal violation of pentagon inequalities in four-state systems
• Nonclassical Structures within the N-qubit Pauli Group
• The quantum maxima for the basic graphs of exclusivity are not reachable in Bell scenarios
• All fundamental non-contextuality inequalities are unique