Effect Algebras, Presheaves, Non-locality and Contextuality

Conference paper

DOI: 10.1007/978-3-662-47666-6_32

Part of the Lecture Notes in Computer Science book series (LNCS, volume 9135)
Cite this paper as:
Staton S., Uijlen S. (2015) Effect Algebras, Presheaves, Non-locality and Contextuality. In: Halldórsson M., Iwama K., Kobayashi N., Speckmann B. (eds) Automata, Languages, and Programming. ICALP 2015. Lecture Notes in Computer Science, vol 9135. Springer, Berlin, Heidelberg

Abstract

Non-locality and contextuality are among the most counterintuitive aspects of quantum theory. They are difficult to study using classical logic and probability theory. In this paper we start with an effect algebraic approach to the study of non-locality and contextuality. We will see how different slices over the category of set valued functors on the natural numbers induce different settings in which non-locality and contextuality can be studied. This includes the Bell, Hardy and Kochen-Specker-type paradoxes. We link this to earlier sheaf theoretic approaches by defining a fully faithful embedding of the category of effect algebras in this presheaf category over the natural numbers.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.University of OxfordOxfordEngland, UK
  2. 2.Radboud UniversityNijmegenThe Netherlands

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