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On graph approaches to contextuality and their role in quantum theory

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	On graph approaches to contextuality and their role in quantum theory/ by Barbara Amaral, Marcelo Terra Cunha.
作者:	Amaral, Barbara.
其他作者:	Terra Cunha, Marcelo.
出版者:	Cham :Springer International Publishing : : 2018.,
面頁冊數:	ix, 135 p. :digital ; : 24 cm.;
Contained By:	Springer eBooks
標題:	Quantum theory. -
電子資源:	http://dx.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. - 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

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

568041
Quantum theory.

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

Dewey Class. No.: 530.12

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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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