On graph approaches to contextuality and their role in quantum theory. (2018)

• Record Type: Book
• Further Information: Note: Barbara Amaral, Marcelo Terra Cunha.
• Authors: Amaral, Barbara; Cunha, Marcelo Terra
• 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
• Publisher Details: Cham, Switzerland : Springer
• Publication Date: 2018
• Extent: 1 online resource
• Subjects: 530.12; Mathematics; Quantum theory; Graph theory; SCIENCE / Energy; SCIENCE / Mechanics / General; SCIENCE / Physics / General; Graph theory; Quantum theory; Mathematics; Quantum Computing; Graph Theory; Quantum Physics; Mathematics -- Graphic Methods; Science -- Quantum Theory; Combinatorics & graph theory; Quantum physics (quantum mechanics & quantum field theory); Mathematical theory of computation; Electronic books
• Languages: English
• ISBNs: 9783319938271; 3319938274
• Related ISBNs: 9783319938264; 3319938266
• Notes: Note: Includes bibliographical references and index.; Note: Online resource; title from PDF title page (SpringerLink, viewed August 2, 2018).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.