Basic exclusivity graphs in quantum correlations

Abstract

A fundamental problem is to understand why quantum theory only violates some noncontextuality (NC) inequalities and identify the physical principles that prevent higher-than-quantum violations. We prove that quantum theory only violates those NC inequalities whose exclusivity graphs contain, as induced subgraphs, odd cycles of length five or more, and/or their complements. In addition, we show that odd cycles are the exclusivity graphs of a well-known family of NC inequalities and that there is also a family of NC inequalities whose exclusivity graphs are the complements of odd cycles. We characterize the maximum noncontextual and quantum values of these inequalities, and provide evidence supporting the conjecture that the maximum quantum violation of these inequalities is exactly singled out by the exclusivity principle.

REVTeX4, 7 pages, 2 figures

References in corpus (12)

• A simple test for hidden variables in spin-1 system
• Experimentally testable state-independent quantum contextuality
• The uncertainty principle determines the non-locality of quantum mechanics
• Local orthogonality as a multipartite principle for quantum correlations
• Preparation contextuality powers parity-oblivious multiplexing
• Computational power of correlations
• Simple explanation of the quantum violation of a fundamental inequality
• Universality of state-independent violation of correlation inequalities for noncontextual theories
• Experimental implementation of a Kochen-Specker set of quantum tests
• Proposed experiment for testing quantum contextuality with neutrons
• Experimental observation of impossible-to-beat quantum advantage on a hybrid photonic system
• Twin inequality for fully contextual quantum correlations

Cited by in corpus (34)

• Kochen-Specker Contextuality
• A Combinatorial Approach to Nonlocality and Contextuality
• Simple Hardy-like proof of quantum contextuality
• Simple method for experimentally testing any form of quantum contextuality
• The exclusivity principle forbids sets of correlations larger than the quantum set
• Necessary and sufficient condition for contextuality from incompatibility
• Minimal true-implies-false and true-implies-true sets of propositions in noncontextual hidden variable theories
• Quantum correlations from simple assumptions
• Multigraph approach to quantum non-locality
• Exclusivity principle and the quantum bound of the Bell inequality
• Quantum Contextuality with Stabilizer States
• Gadget structures in proofs of the Kochen-Specker theorem
• Extensions of Hardy-type true-implies-false gadgets to classically obtain indistinguishability
• Testing noncontextuality inequalities that are building blocks of quantum correlations
• Orthogonal Representation of Graphs
• Faithful orthogonal representations of graphs from partition logics
• Characterising the Performance of XOR Games and the Shannon Capacity of Graphs
• Experimental demonstration of the connection between quantum contextuality and graph theory
• Bounding quantum theory with the exclusivity principle in a two-city experiment
• Local Orthogonality provides better upper bound for Hardy's nonlocality
• Local certification of programmable quantum devices of arbitrary high dimensionality
• The Exclusivity Principle and the Set of Quantum Correlations
• The rank of contextuality
• Large violations in Kochen Specker contextuality and their applications
• State-independent quantum contextuality with projectors of nonunit rank
• From the problem of Future Contingents to Peres-Mermin square experiments: An introductory review to Contextuality
• Bosonic Indistinguishability-Dependent Contextuality
• Quantum Logic and Quantum Reconstruction
• The quantum maxima for the basic graphs of exclusivity are not reachable in Bell scenarios
• Unexpected consequences of Post-Quantum theories in the graph-theoretical approach to correlations
• Nonclassicality of induced coherence witnessed by contextuality
• Graph theoretic quantum contextuality and unextendible Product Bases
• All fundamental non-contextuality inequalities are unique
• On Orthogonal Vector Edge Coloring