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Contextuality, Cohomology and Paradox

Authors Samson Abramsky, Rui Soares Barbosa, Kohei Kishida, Raymond Lal, Shane Mansfield

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Samson Abramsky
Rui Soares Barbosa
Kohei Kishida
Raymond Lal
Shane Mansfield

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Samson Abramsky, Rui Soares Barbosa, Kohei Kishida, Raymond Lal, and Shane Mansfield. Contextuality, Cohomology and Paradox. In 24th EACSL Annual Conference on Computer Science Logic (CSL 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 41, pp. 211-228, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015) https://doi.org/10.4230/LIPIcs.CSL.2015.211

Abstract

Contextuality is a key feature of quantum mechanics that provides an important non-classical resource for quantum information and computation.  Abramsky and Brandenburger used sheaf theory to give a general treatment of contextuality in quantum theory [New Journal of Physics 13 (2011) 113036]. However, contextual phenomena are found in other fields as well, for example database theory. In this paper, we shall develop this unified view of contextuality. We provide two main contributions: firstly, we expose a remarkable connection between contexuality and logical paradoxes; secondly, we show that an important class of contextuality arguments has a topological origin. More specifically, we show that "All-vs-Nothing" proofs of contextuality are witnessed by cohomological obstructions.

Subject Classification

Keywords
  • Quantum mechanics
  • contextuality
  • sheaf theory
  • cohomology
  • logical paradoxes

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