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oai:drops-oai.dagstuhl.de:6248 2024-03-06T10:37:53Z ddc:004 open_access

Logic of Local Inference for Contextuality in Quantum Physics and Beyond Kishida, Kohei Contextuality quantum mechanics regular category regular logic separated presheaf 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Kohei Kishida 2016 Is Part Of LIPIcs, Volume 55, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ICALP.2016.113 urn:nbn:de:0030-drops-62484 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.113 eng https://creativecommons.org/licenses/by/3.0/legalcode