{"id":1280,"date":"2023-01-05T12:07:18","date_gmt":"2023-01-05T10:07:18","guid":{"rendered":"https:\/\/webs.uab.cat\/giq\/seminar\/an-invertible-map-between-bell-non-local-and-contextuality-scenarios\/"},"modified":"2023-01-05T12:07:18","modified_gmt":"2023-01-05T10:07:18","slug":"an-invertible-map-between-bell-non-local-and-contextuality-scenarios","status":"publish","type":"seminar","link":"https:\/\/webs.uab.cat\/giq\/seminar\/an-invertible-map-between-bell-non-local-and-contextuality-scenarios\/","title":{"rendered":"An invertible map between Bell non-local and contextuality scenarios"},"content":{"rendered":"<div><span style=\"font-family:Calibri,Arial,Helvetica,sans-serif;font-size:12pt;color:rgb(0,0,0);background-color:rgb(255,255,255)\">Bell non-locality and generalised contextuality are both fundamental quantum phenomena that can tell classical and quantum theories apart in an a priori theory-independent manner. At first sight the two notions might appear unrelated, as Bell non-locality addresses bipartite systems, while generalised contextuality addresses single systems. It has, however, been noticed before that Bell non-locality can be connected to generalised contextuality in some simple cases. In this work, we completely formalise this connection. In particular, we map every correlation in a Bell scenario to a behaviour in an indexed family of contextuality scenarios in an invertible way. Furthermore, our construction maps every quantum realisation of a correlation to a quantum realisation of a behaviour in the corresponding contextuality scenario. As such, the set of quantum correlations in a given Bell scenario is isomorphic to an indexed family of quantum contextual behaviours. Furthermore, the set of local correlations is isomorphic to the set of non-contextual behaviours and the set of no-signalling correlations is isomorphic to the set of contextual behaviours. Our map allows us to derive some fundamental properties of the set of quantum contextual behaviours: In general, the membership problem of this set is undecidable, it is not closed, and finite-dimensional quantum systems are not sufficient for realising every behaviour. Finally, due to the result MIP*=RE, there exist no computable sequence of outer approximations of the quantum contextual set that converges to the set itself.<\/span><\/div>\n<div>\n<div style=\"font-family:Calibri,Arial,Helvetica,sans-serif;font-size:12pt;color:rgb(0,0,0)\">&nbsp;<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Bell non-locality and generalised contextuality are both fundamental quantum phenomena that can tell classical and quantum theories apart in an a priori theory-independent manner. At first sight the two notions might appear unrelated, as Bell non-locality addresses bipartite systems, while generalised contextuality addresses single systems. It has, however, been noticed before that Bell non-locality can [&hellip;]<\/p>\n","protected":false},"author":20,"featured_media":0,"template":"","class_list":["post-1280","seminar","type-seminar","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/webs.uab.cat\/giq\/wp-json\/wp\/v2\/seminar\/1280","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/webs.uab.cat\/giq\/wp-json\/wp\/v2\/seminar"}],"about":[{"href":"https:\/\/webs.uab.cat\/giq\/wp-json\/wp\/v2\/types\/seminar"}],"author":[{"embeddable":true,"href":"https:\/\/webs.uab.cat\/giq\/wp-json\/wp\/v2\/users\/20"}],"wp:attachment":[{"href":"https:\/\/webs.uab.cat\/giq\/wp-json\/wp\/v2\/media?parent=1280"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}