On Graph Approaches to Contextuality and their Role in Quantum Theory

Barbara Amaral, Marcelo Terra Cunha (Autoren)

Buch | Softcover

IX, 135 Seiten

2018 | 1st ed. 2018
Springer International Publishing (Verlag)
978-3-319-93826-4 (ISBN)

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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.

Barbara Amaral is an associate professor of mathematics at the Federal University of São João del-Rei, Brazil, and a visiting researcher at the International Institute of Physics, Brazil. Her PhD thesis ("The Exclusivity Principle and the Set of Quantum Correlations", 2014) was awarded the Best Thesis Prize in Science and Technology by the Federal University of Minas Gerais, Brazil, from where she also graduated. She has co-authored a book on quantum theory for mathematics students (in Portuguese) as well as a number of research papers on the topic.

Chapter 01- Introduction.- Chapter 02- Contextuality: the Compatibility-Hypergraph Approach.- Chapter 03- Contextuality: the Exclusivity-Graph Approach.- Chapter 04- The Exclusivity Principle and Its Consequences.- Appendix A- State-independent proofs of the Bell-Kochen-Specker Theorem.

Erscheinungsdatum	10.08.2018
Reihe/Serie	SpringerBriefs in Mathematics
Zusatzinfo	IX, 135 p. 42 illus., 25 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	235 g
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
	Mathematik / Informatik ► Mathematik ► Graphentheorie
	Naturwissenschaften ► Physik / Astronomie ► Quantenphysik
	Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
Schlagworte	Contextuality • graph-theoretical invariants • graph theory • Invariants • Quantum Computing • Quantum Correlations • Quantum Theory
ISBN-10	3-319-93826-6 / 3319938266
ISBN-13	978-3-319-93826-4 / 9783319938264
Zustand	Neuware