BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Samson Abramsky DTSTART:20210311T170000Z DTEND:20210311T180000Z DTSTAMP:20260409T092028Z UID:ToposInstituteColloquium/4 DESCRIPTION:Title: The logic of contextuality\nby Samson Abramsky as par t of Topos Institute Colloquium\n\n\nAbstract\n(joint work with Rui Soares Barbosa)\n\nContextuality is a key signature of quantum non-classicality\ , which has been shown to play a central role in enabling quantum advantag e for a wide range of information-processing and computational tasks.\nWe study the logic of contextuality from a structural point of view\, in the setting of partial Boolean algebras introduced by Kochen and Specker in th eir seminal work.\nThese contrast with traditional quantum logic a la Birk hoff--von Neumann\nin that operations such as conjunction and disjunction are partial\, only being defined in the domain where they are physically m eaningful.\n\nWe study how this setting relates to current work on context uality such as the sheaf-theoretic and graph-theoretic approaches.\nWe int roduce a general free construction extending the commeasurability relation on a partial Boolean algebra\, i.e. the domain of definition of the binar y logical operations.\nThis construction has a surprisingly broad range of uses.\nWe apply it in the study of a number of issues\, including:\n\n- e stablishing the connection between the abstract measurement scenarios stud ied in the contextuality literature and the setting of partial Boolean alg ebras\;\n\n- formulating various contextuality properties in this setting\ , including probabilistic contextuality as well as the strong\, state-inde pendent notion of contextuality given by Kochen--Specker paradoxes\, which are logically contradictory statements validated by partial Boolean algeb ras\, specifically those arising from quantum mechanics\;\n\n- investigati ng a Logical Exclusivity Principle\, and its relation to the Probabilistic Exclusivity Principle widely studied in recent work on contextuality\nas a step towards closing in on the set of quantum-realisable correlations\;\ n\n- developing some work towards a logical characterisation of the Hilber t space tensor product\, using logical exclusivity to capture some of its salient quantum features.\n LOCATION:https://researchseminars.org/talk/ToposInstituteColloquium/4/ END:VEVENT END:VCALENDAR