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On Graph Approaches to Contextuality and their Role in Quantum Theory

Record Type:	Language materials, printed : Monograph/item
Title/Author:	On Graph Approaches to Contextuality and their Role in Quantum Theory/ by Barbara Amaral, Marcelo Terra Cunha.
Author:	Amaral, Barbara.
other author:	Terra Cunha, Marcelo.
Description:	IX, 135 p. 42 illus., 25 illus. in color.online resource. :
Contained By:	Springer Nature eBook
Subject:	Quantum computers. -
Online resource:	https://doi.org/10.1007/978-3-319-93827-1
ISBN:	9783319938271

On Graph Approaches to Contextuality and their Role in Quantum Theory
Amaral, Barbara.

On Graph Approaches to Contextuality and their Role in Quantum Theory[electronic resource] /by Barbara Amaral, Marcelo Terra Cunha. - 1st ed. 2018. - IX, 135 p. 42 illus., 25 illus. in color.online resource. - SpringerBriefs in Mathematics,2191-8198. - SpringerBriefs in Mathematics,.

Chapter 01- Introduction -- Chapter 02- Contextuality: the Compatibility-Hypergraph Approach -- Chapter 03- Contextuality: the Exclusivity-Graph Approach -- Chapter 04- The Exclusivity Principle and Its Consequences -- Appendix A- State-independent proofs of the Bell-Kochen-Specker Theorem.

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.

ISBN: 9783319938271

Standard No.: 10.1007/978-3-319-93827-1doiSubjects--Topical Terms:

564139
Quantum computers.

LC Class. No.: QA76.889

Dewey Class. No.: 004.1

On Graph Approaches to Contextuality and their Role in Quantum Theory
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520 $a 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.
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