License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CSL.2015.211
URN: urn:nbn:de:0030-drops-54166
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2015/5416/
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Abramsky, Samson ; Soares Barbosa, Rui ; Kishida, Kohei ; Lal, Raymond ; Mansfield, Shane

Contextuality, Cohomology and Paradox

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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.

BibTeX - Entry

@InProceedings{abramsky_et_al:LIPIcs:2015:5416,
  author =	{Samson Abramsky and Rui Soares Barbosa and Kohei Kishida and Raymond Lal and Shane Mansfield},
  title =	{{Contextuality, Cohomology and Paradox}},
  booktitle =	{24th EACSL Annual Conference on Computer Science Logic (CSL 2015)},
  pages =	{211--228},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-90-3},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{41},
  editor =	{Stephan Kreutzer},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2015/5416},
  URN =		{urn:nbn:de:0030-drops-54166},
  doi =		{10.4230/LIPIcs.CSL.2015.211},
  annote =	{Keywords: Quantum mechanics, contextuality, sheaf theory, cohomology, logical paradoxes}
}

Keywords: Quantum mechanics, contextuality, sheaf theory, cohomology, logical paradoxes
Collection: 24th EACSL Annual Conference on Computer Science Logic (CSL 2015)
Issue Date: 2015
Date of publication: 07.09.2015

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