Graph-theoretic strengths of contextuality

Abstract

Cabello-Severini-Winter and Abramsky-Hardy (building on the framework of Abramsky-Brandenburger) both provide classes of Bell and contextuality inequalities for very general experimental scenarios using vastly different mathematical techniques. We review both approaches, carefully detail the links between them, and give simple, graph-theoretic methods for finding inequality-free proofs of nonlocality and contextuality and for finding states exhibiting strong nonlocality and/or contextuality. Finally, we apply these methods to concrete examples in stabilizer quantum mechanics relevant to understanding contextuality as a resource in quantum computation.

arXiv comment13 pages; significantly rewritten

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Cited by in corpus (10)

• Quantum Advantage from Sequential-Transformation Contextuality
• Contextuality Test of the Nonclassicality of Variational Quantum Eigensolvers
• Contextual Subspace Variational Quantum Eigensolver
• Classical Simulation of Noncontextual Pauli Hamiltonians
• Unitary Partitioning and the Contextual Subspace Variational Quantum Eigensolver
• On the origin of nonclassicality in single systems
• From the problem of Future Contingents to Peres-Mermin square experiments: An introductory review to Contextuality
• Contextuality, Witness of Quantum Weirdness
• Contextuality from the vacuum
• The Interplay between Quantum Contextuality and Wigner Negativity