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The Resource On graph approaches to contextuality and their role in quantum theory, Barbara Amaral, Marcelo Terra Cunha

On graph approaches to contextuality and their role in quantum theory, Barbara Amaral, Marcelo Terra Cunha

Creator
Author
Contributor
Summary
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.--
Language
eng
Work
Publication
Extent
1 online resource.
Contents
  • Intro; Preface; Contents; 1 Introduction; 1.1 States and Measurements; 1.1.1 Repeatability and Compatibility; 1.1.2 Classical Probability Theory; 1.1.3 Quantum Probability Theory; 1.2 Completing a Probabilistic Model; 1.2.1 The Assumption of Noncontextuality; 1.3 Outline of the Book; 2 Contextuality: The Compatibility-Hypergraph Approach; 2.1 Compatibility Scenarios; 2.1.1 Bell Scenarios; 2.2 Probability Distributions and Physical Theories; 2.2.1 Classical Realisations and Noncontextuality; 2.2.2 Quantum Realisations; 2.3 Noncontextuality Inequalities; 2.3.1 The CHSH Inequality
  • 2.3.2 The KCBS Inequality2.3.3 The n-Cycle Inequalities; 2.4 The Exclusivity Graph; 2.4.1 Vertex-Weighted Exclusivity Graph; 2.5 The Geometry of the Case H=G; 2.5.1 Description of the Nondisturbing, Quantum and Noncontextual Behaviours; 2.5.2 The Cut Polytope; 2.5.3 Correlation Functions; 2.5.4 The Eliptope and the Set of Quantum Behaviours; 2.6 Sheaf Theory and Contextuality; 2.6.1 Bundle Diagrams; 2.7 Final Remarks; 3 Contextuality: The Exclusivity-Graph Approach; 3.1 The Exclusivity Graph; 3.1.1 Classical Noncontextual Behaviours; 3.1.2 Quantum Behaviours; 3.1.3 The Exclusivity Principle
  • 4.3 The Exclusivity Principle Forbids Behaviours Outside the Quantum Set4.4 Other Graph Operations; 4.4.1 Direct Cosum; 4.4.2 Twinning, Partial Twinning and Duplication; 4.4.3 Vertex-Transitive Graphs Obtained from C5; 4.5 The Exclusivity Principle in the Exclusivity-Hypergraph Approach; 4.5.1 The Foulis-Randall Product; 4.5.2 Activation Effects of the E-Principle; 4.6 Final Remarks; Appendix A State-Independent Proofs of the Bell-Kochen-Specker Theorem; A.1 von Neumann; A.1.1 von Neumann's Assumptions; A.2 Gleason's Lemma; A.2.1 Using Gleason's Lemma to Discard Completions of Quantum Theory
  • A.2.2 The H̀̀idden'' Assumption of NoncontextualityA.3 Kochen and Specker's Proof; A.4 Other Additive Proofs of the Bell-Kochen-Specker Theorem; A.4.1 P-33; A.4.2 Cabello's Proof with 18 Vectors; A.4.3 Cabello's Proof with 21 Vectors; A.5 Multiplicative Proofs of the Bell-Kochen-Specker Theorem; A.5.1 The Peres Mermin Square; A.5.2 A Simple Proof in Dimension 8; A.6 Yu and Oh's Proof with 13 Vectors; A.7 A Contextual Completion; References; Index
Isbn
9783319938271
Instance
Label
On graph approaches to contextuality and their role in quantum theory
Title
On graph approaches to contextuality and their role in quantum theory
Statement of responsibility
Barbara Amaral, Marcelo Terra Cunha
Creator
Contributor
Author
Subject
Language
eng
Summary
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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Assigning source
Provided by publisher
Cataloging source
N$T
http://library.link/vocab/creatorName
Amaral, Barbara
Dewey number
530.12
Index
index present
LC call number
QC174.12
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorName
Cunha, Marcelo Terra
Series statement
SpringerBriefs in mathematics
http://library.link/vocab/subjectName
  • Quantum theory
  • Graph theory
Label
On graph approaches to contextuality and their role in quantum theory, Barbara Amaral, Marcelo Terra Cunha
Instantiates
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Intro; Preface; Contents; 1 Introduction; 1.1 States and Measurements; 1.1.1 Repeatability and Compatibility; 1.1.2 Classical Probability Theory; 1.1.3 Quantum Probability Theory; 1.2 Completing a Probabilistic Model; 1.2.1 The Assumption of Noncontextuality; 1.3 Outline of the Book; 2 Contextuality: The Compatibility-Hypergraph Approach; 2.1 Compatibility Scenarios; 2.1.1 Bell Scenarios; 2.2 Probability Distributions and Physical Theories; 2.2.1 Classical Realisations and Noncontextuality; 2.2.2 Quantum Realisations; 2.3 Noncontextuality Inequalities; 2.3.1 The CHSH Inequality
  • 2.3.2 The KCBS Inequality2.3.3 The n-Cycle Inequalities; 2.4 The Exclusivity Graph; 2.4.1 Vertex-Weighted Exclusivity Graph; 2.5 The Geometry of the Case H=G; 2.5.1 Description of the Nondisturbing, Quantum and Noncontextual Behaviours; 2.5.2 The Cut Polytope; 2.5.3 Correlation Functions; 2.5.4 The Eliptope and the Set of Quantum Behaviours; 2.6 Sheaf Theory and Contextuality; 2.6.1 Bundle Diagrams; 2.7 Final Remarks; 3 Contextuality: The Exclusivity-Graph Approach; 3.1 The Exclusivity Graph; 3.1.1 Classical Noncontextual Behaviours; 3.1.2 Quantum Behaviours; 3.1.3 The Exclusivity Principle
  • 4.3 The Exclusivity Principle Forbids Behaviours Outside the Quantum Set4.4 Other Graph Operations; 4.4.1 Direct Cosum; 4.4.2 Twinning, Partial Twinning and Duplication; 4.4.3 Vertex-Transitive Graphs Obtained from C5; 4.5 The Exclusivity Principle in the Exclusivity-Hypergraph Approach; 4.5.1 The Foulis-Randall Product; 4.5.2 Activation Effects of the E-Principle; 4.6 Final Remarks; Appendix A State-Independent Proofs of the Bell-Kochen-Specker Theorem; A.1 von Neumann; A.1.1 von Neumann's Assumptions; A.2 Gleason's Lemma; A.2.1 Using Gleason's Lemma to Discard Completions of Quantum Theory
  • A.2.2 The H̀̀idden'' Assumption of NoncontextualityA.3 Kochen and Specker's Proof; A.4 Other Additive Proofs of the Bell-Kochen-Specker Theorem; A.4.1 P-33; A.4.2 Cabello's Proof with 18 Vectors; A.4.3 Cabello's Proof with 21 Vectors; A.5 Multiplicative Proofs of the Bell-Kochen-Specker Theorem; A.5.1 The Peres Mermin Square; A.5.2 A Simple Proof in Dimension 8; A.6 Yu and Oh's Proof with 13 Vectors; A.7 A Contextual Completion; References; Index
Dimensions
unknown
Extent
1 online resource.
File format
unknown
Form of item
online
Isbn
9783319938271
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
  • on1046977430
  • (OCoLC)1046977430
Label
On graph approaches to contextuality and their role in quantum theory, Barbara Amaral, Marcelo Terra Cunha
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Intro; Preface; Contents; 1 Introduction; 1.1 States and Measurements; 1.1.1 Repeatability and Compatibility; 1.1.2 Classical Probability Theory; 1.1.3 Quantum Probability Theory; 1.2 Completing a Probabilistic Model; 1.2.1 The Assumption of Noncontextuality; 1.3 Outline of the Book; 2 Contextuality: The Compatibility-Hypergraph Approach; 2.1 Compatibility Scenarios; 2.1.1 Bell Scenarios; 2.2 Probability Distributions and Physical Theories; 2.2.1 Classical Realisations and Noncontextuality; 2.2.2 Quantum Realisations; 2.3 Noncontextuality Inequalities; 2.3.1 The CHSH Inequality
  • 2.3.2 The KCBS Inequality2.3.3 The n-Cycle Inequalities; 2.4 The Exclusivity Graph; 2.4.1 Vertex-Weighted Exclusivity Graph; 2.5 The Geometry of the Case H=G; 2.5.1 Description of the Nondisturbing, Quantum and Noncontextual Behaviours; 2.5.2 The Cut Polytope; 2.5.3 Correlation Functions; 2.5.4 The Eliptope and the Set of Quantum Behaviours; 2.6 Sheaf Theory and Contextuality; 2.6.1 Bundle Diagrams; 2.7 Final Remarks; 3 Contextuality: The Exclusivity-Graph Approach; 3.1 The Exclusivity Graph; 3.1.1 Classical Noncontextual Behaviours; 3.1.2 Quantum Behaviours; 3.1.3 The Exclusivity Principle
  • 4.3 The Exclusivity Principle Forbids Behaviours Outside the Quantum Set4.4 Other Graph Operations; 4.4.1 Direct Cosum; 4.4.2 Twinning, Partial Twinning and Duplication; 4.4.3 Vertex-Transitive Graphs Obtained from C5; 4.5 The Exclusivity Principle in the Exclusivity-Hypergraph Approach; 4.5.1 The Foulis-Randall Product; 4.5.2 Activation Effects of the E-Principle; 4.6 Final Remarks; Appendix A State-Independent Proofs of the Bell-Kochen-Specker Theorem; A.1 von Neumann; A.1.1 von Neumann's Assumptions; A.2 Gleason's Lemma; A.2.1 Using Gleason's Lemma to Discard Completions of Quantum Theory
  • A.2.2 The H̀̀idden'' Assumption of NoncontextualityA.3 Kochen and Specker's Proof; A.4 Other Additive Proofs of the Bell-Kochen-Specker Theorem; A.4.1 P-33; A.4.2 Cabello's Proof with 18 Vectors; A.4.3 Cabello's Proof with 21 Vectors; A.5 Multiplicative Proofs of the Bell-Kochen-Specker Theorem; A.5.1 The Peres Mermin Square; A.5.2 A Simple Proof in Dimension 8; A.6 Yu and Oh's Proof with 13 Vectors; A.7 A Contextual Completion; References; Index
Dimensions
unknown
Extent
1 online resource.
File format
unknown
Form of item
online
Isbn
9783319938271
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
  • on1046977430
  • (OCoLC)1046977430

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