Contextuality, Cohomology and Paradox

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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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.
Original languageEnglish
Title of host publication24th EACSL Annual Conference on Computer Science Logic (CSL 2015)
EditorsStephan Kreutzer
Place of PublicationDagstuhl, Germany
PublisherSchloss Dagstuhl - Leibniz-Zentrum fuer Informatik, Germany
Pages211-228
Number of pages18
Volume41
ISBN (Print)978-3-939897-90-3
DOIs
Publication statusPublished - 2015
Externally publishedYes
Event24th EACSL Annual Conference on Computer Science Logic - Technische Universität Berlin, Berlin, Germany
Duration: 7 Sep 201510 Sep 2015
Conference number: 24
http://logic.las.tu-berlin.de/csl2015/

Publication series

NameLeibniz International Proceedings in Informatics (LIPIcs)
PublisherSchloss Dagstuhl--Leibniz-Zentrum fuer Informatik

Conference

Conference24th EACSL Annual Conference on Computer Science Logic
Abbreviated titleCSL 2015
Country/TerritoryGermany
CityBerlin
Period7/09/1510/09/15
Internet address

Keywords

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

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