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On Graph Approaches to Contextuality and their Role in Quantum Theory

  • Barbara Amaral
  • Marcelo  Terra Cunha

Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Barbara Amaral, Marcelo Terra Cunha
    Pages 1-12
  3. Barbara Amaral, Marcelo Terra Cunha
    Pages 13-48
  4. Barbara Amaral, Marcelo Terra Cunha
    Pages 49-74
  5. Barbara Amaral, Marcelo Terra Cunha
    Pages 75-100
  6. Back Matter
    Pages 101-135

About this book

Introduction

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.


Keywords

contextuality invariants quantum correlations quantum theory graph-theoretical invariants graph theory quantum computing

Authors and affiliations

  • Barbara Amaral
    • 1
  • Marcelo  Terra Cunha
    • 2
  1. 1.Department of Statistics, Physics and MathematicsFederal University of São João del-ReiOuro BrancoBrazil
  2. 2.IMECC – Department of Applied MathematicsUniversity of CampinasCampinasBrazil

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-93827-1
  • Copyright Information The Author(s), under exclusive licence to Springer Nature Switzerland AG 2018
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-93826-4
  • Online ISBN 978-3-319-93827-1
  • Series Print ISSN 2191-8198
  • Series Online ISSN 2191-8201
  • Buy this book on publisher's site