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
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The item On graph approaches to contextuality and their role in quantum theory, Barbara Amaral, Marcelo Terra Cunha represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.This item is available to borrow from 1 library branch.
Resource Information
The item On graph approaches to contextuality and their role in quantum theory, Barbara Amaral, Marcelo Terra Cunha represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.
This item is available to borrow from 1 library branch.
 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 noncontextuality hypothesis, the book describes contextuality scenarios using compatibility hypergraphs. It then introduces the exclusivity graph approach, which relates a number of important graphtheoretical concepts to contextuality. It also presents open problems such as the socalled Exclusivity Principle, as well as a selection of important topics, like sheaftheoretical approach, hypergraph approach, and alternative proofs of contextuality.
 Language
 eng
 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 CompatibilityHypergraph 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 nCycle Inequalities; 2.4 The Exclusivity Graph; 2.4.1 VertexWeighted 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 ExclusivityGraph 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 VertexTransitive Graphs Obtained from C5; 4.5 The Exclusivity Principle in the ExclusivityHypergraph Approach; 4.5.1 The FoulisRandall Product; 4.5.2 Activation Effects of the EPrinciple; 4.6 Final Remarks; Appendix A StateIndependent Proofs of the BellKochenSpecker 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 BellKochenSpecker Theorem; A.4.1 P33; A.4.2 Cabello's Proof with 18 Vectors; A.4.3 Cabello's Proof with 21 Vectors; A.5 Multiplicative Proofs of the BellKochenSpecker 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
 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
 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 noncontextuality hypothesis, the book describes contextuality scenarios using compatibility hypergraphs. It then introduces the exclusivity graph approach, which relates a number of important graphtheoretical concepts to contextuality. It also presents open problems such as the socalled Exclusivity Principle, as well as a selection of important topics, like sheaftheoretical approach, hypergraph approach, and alternative proofs of contextuality.
 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
 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 CompatibilityHypergraph 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 nCycle Inequalities; 2.4 The Exclusivity Graph; 2.4.1 VertexWeighted 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 ExclusivityGraph 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 VertexTransitive Graphs Obtained from C5; 4.5 The Exclusivity Principle in the ExclusivityHypergraph Approach; 4.5.1 The FoulisRandall Product; 4.5.2 Activation Effects of the EPrinciple; 4.6 Final Remarks; Appendix A StateIndependent Proofs of the BellKochenSpecker 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 BellKochenSpecker Theorem; A.4.1 P33; A.4.2 Cabello's Proof with 18 Vectors; A.4.3 Cabello's Proof with 21 Vectors; A.5 Multiplicative Proofs of the BellKochenSpecker 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
 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 CompatibilityHypergraph 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 nCycle Inequalities; 2.4 The Exclusivity Graph; 2.4.1 VertexWeighted 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 ExclusivityGraph 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 VertexTransitive Graphs Obtained from C5; 4.5 The Exclusivity Principle in the ExclusivityHypergraph Approach; 4.5.1 The FoulisRandall Product; 4.5.2 Activation Effects of the EPrinciple; 4.6 Final Remarks; Appendix A StateIndependent Proofs of the BellKochenSpecker 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 BellKochenSpecker Theorem; A.4.1 P33; A.4.2 Cabello's Proof with 18 Vectors; A.4.3 Cabello's Proof with 21 Vectors; A.5 Multiplicative Proofs of the BellKochenSpecker 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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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.liverpool.ac.uk/portal/Ongraphapproachestocontextualityandtheir/XIE4jLvrdR8/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.liverpool.ac.uk/portal/Ongraphapproachestocontextualityandtheir/XIE4jLvrdR8/">On graph approaches to contextuality and their role in quantum theory, Barbara Amaral, Marcelo Terra Cunha</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.liverpool.ac.uk/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.liverpool.ac.uk/">University of Liverpool</a></span></span></span></span></div>