# A Combinatorial Approach to Nonlocality and Contextuality

@article{Acn2015ACA, title={A Combinatorial Approach to Nonlocality and Contextuality}, author={Antonio Ac{\'i}n and Tobias Fritz and Anthony Leverrier and Ana Bel{\'e}n Sainz}, journal={Communications in Mathematical Physics}, year={2015}, volume={334}, pages={533-628} }

AbstractSo far, most of the literature on (quantum) contextuality and the Kochen–Specker theorem seems either to concern particular examples of contextuality, or be considered as quantum logic. Here, we develop a general formalism for contextuality scenarios based on the combinatorics of hypergraphs, which significantly refines a similar recent approach by Cabello, Severini and Winter (CSW). In contrast to CSW, we explicitly include the normalization of probabilities, which gives us a much…

## 156 Citations

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This chapter presents the compatibility-graph approach, where the main concerns are the compatibility relations of a finite set of measurements and the relation between noncontextuality inequalities and the exclusivity graph of the contextuality scenario and how the classical and quantum bounds to these inequalities are related to graph invariants of this graph.

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### Contextuality, Cohomology and Paradox

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(Dated: Quantum contextuality is one of the most recognized resources in quantum communication and computing scenarios. We provide a new quantiﬁer of this resource, the rank of contextuality (RC). We…

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