Logic of local inference for contextuality in quantum physics and beyond

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

Abstract

Contextuality in quantum physics provides a key resource for quantum information and computation. The topological approach in [Abramsky and Brandenburger, New J. Phys., 2011, Abramsky et al., CSL 2015, 2015] characterizes contextuality as "global inconsistency" coupled with "local consistency", revealing it to be a phenomenon also found in many other fields. This has yielded a logical method of detecting and proving the "global inconsistency" part of contextuality. Our goal is to capture the other, "local consistency" part, which requires a novel approach to logic that is sensitive to the topology of contexts. To achieve this, we formulate a logic of local inference by using context-sensitive theories and models in regular categories. This provides a uniform framework for local consistency, and lays a foundation for high-level methods of detecting, proving, and moreover using contextuality as computational resource.

Original languageEnglish (US)
Title of host publication43rd International Colloquium on Automata, Languages, and Programming, ICALP 2016
EditorsYuval Rabani, Ioannis Chatzigiannakis, Davide Sangiorgi, Michael Mitzenmacher
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959770132
DOIs
StatePublished - Aug 1 2016
Externally publishedYes
Event43rd International Colloquium on Automata, Languages, and Programming, ICALP 2016 - Rome, Italy
Duration: Jul 12 2016Jul 15 2016

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume55
ISSN (Print)1868-8969

Other

Other43rd International Colloquium on Automata, Languages, and Programming, ICALP 2016
CountryItaly
CityRome
Period7/12/167/15/16

Keywords

  • Contextuality
  • Quantum mechanics
  • Regular category
  • Regular logic
  • Separated presheaf

ASJC Scopus subject areas

  • Software

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  • Cite this

    Kishida, K. (2016). Logic of local inference for contextuality in quantum physics and beyond. In Y. Rabani, I. Chatzigiannakis, D. Sangiorgi, & M. Mitzenmacher (Eds.), 43rd International Colloquium on Automata, Languages, and Programming, ICALP 2016 [113] (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 55). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.ICALP.2016.113