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Table of 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 ``Hidden'' 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
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 ``Hidden'' 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