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Amaral B., Cunha M.T. On Graph Approaches to Contextuality and their Role in Quantum Theory

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Amaral B., Cunha M.T. On Graph Approaches to Contextuality and their Role in Quantum Theory
Springer, 2018. — 144 p. — (SpringerBriefs in Mathematics). — ISBN 3319938266.
This book explores two of the most striking features of quantum theory – contextuality and nonlocality – using a formulation based on graph theory. Quantum theory provides a set of rules to predict probabilities of different outcomes in different experimental settings, and both contextuality and nonlocality play a fundamental role in interpreting the outcomes. In this work, the authors highlight how the graph approach can lead to a better understanding of this theory and its applications. After presenting basic definitions and explaining the non-contextuality hypothesis, the book describes contextuality scenarios using compatibility hypergraphs. It then introduces the exclusivity graph approach, which relates a number of important graph-theoretical concepts to contextuality. It also presents open problems such as the so-called Exclusivity Principle, as well as a selection of important topics, like sheaf-theoretical approach, hypergraph approach, and alternative proofs of contextuality.
Table of contents
Introduction
Contextuality: The Compatibility-Hypergraph Approach
Contextuality: The Exclusivity-Graph Approach
The Exclusivity Principle and Its Consequences
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