EAN: 9783319938264

SPRINGERBRIEFS IN MATHEMATICS ON GRAPH APPROA...

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.

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