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On graph approaches to contextuality...

Amaral, Barbara.

On graph approaches to contextuality and their role in quantum theory

Record Type:	Electronic resources : Monograph/item
Title/Author:	On graph approaches to contextuality and their role in quantum theoryby Barbara Amaral, Marcelo Terra Cunha.
Author:	Amaral, Barbara.
other author:	Terra Cunha, Marcelo.
Published:	Cham :Springer International Publishing :2018.
Description:	ix, 135 p. :digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Quantum theory.
Online resource:	http://dx.doi.org/10.1007/978-3-319-93827-1
ISBN:	9783319938271$q(electronic bk.)

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. - Cham :Springer International Publishing :2018. - ix, 135 p. :digital ;24 cm. - 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$q(electronic bk.)

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

199020
Quantum theory.

LC Class. No.: QC174.12 / .A437 2018

Dewey Class. No.: 530.12

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245 1 0 $a On graph approaches to contextuality and their role in quantum theory $h [electronic resource] / $c by Barbara Amaral, Marcelo Terra Cunha.
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300 $a ix, 135 p. : $b digital ; $c 24 cm.
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505 0 $a 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.
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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