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.ICALP.2016.113
URN: urn:nbn:de:0030-drops-62484
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6248/
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Kishida, Kohei

Logic of Local Inference for Contextuality in Quantum Physics and Beyond

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LIPIcs-ICALP-2016-113.pdf (0.5 MB)

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.

BibTeX - Entry

@InProceedings{kishida:LIPIcs:2016:6248,
  author =	{Kohei Kishida},
  title =	{{Logic of Local Inference for Contextuality in Quantum Physics and Beyond}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{113:1--113:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Ioannis Chatzigiannakis and Michael Mitzenmacher and Yuval Rabani and Davide Sangiorgi},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6248},
  URN =		{urn:nbn:de:0030-drops-62484},
  doi =		{10.4230/LIPIcs.ICALP.2016.113},
  annote =	{Keywords: Contextuality, quantum mechanics, regular category, regular logic, separated presheaf}
}

Keywords: Contextuality, quantum mechanics, regular category, regular logic, separated presheaf
Collection: 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)
Issue Date: 2016
Date of publication: 23.08.2016

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