On Graph Approaches to Contextuality and their Role in Quantum Theory
Author | : Barbara Amaral |
Publisher | : Springer |
Total Pages | : 144 |
Release | : 2018-07-28 |
ISBN-10 | : 9783319938271 |
ISBN-13 | : 3319938274 |
Rating | : 4/5 (71 Downloads) |
Download or read book On Graph Approaches to Contextuality and their Role in Quantum Theory written by Barbara Amaral and published by Springer. This book was released on 2018-07-28 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.