{"id":2116,"date":"2023-07-19T14:38:26","date_gmt":"2023-07-19T12:38:26","guid":{"rendered":"https:\/\/webs.uab.cat\/giq\/?post_type=seminar&#038;p=2116"},"modified":"2023-07-19T14:38:27","modified_gmt":"2023-07-19T12:38:27","slug":"towards-p-adic-quantum-information-theory","status":"publish","type":"seminar","link":"https:\/\/webs.uab.cat\/giq\/seminar\/towards-p-adic-quantum-information-theory\/","title":{"rendered":"Towards p-adic Quantum Information Theory"},"content":{"rendered":"\n<p>Within the framework of quantum mechanics over a quadratic extension of the non-Archimedean field of p-adic\u00a0numbers, we provide\u00a0a general definition of a quantum state relying on a general algebraic approach and on a p-adic\u00a0model of probability theory. As in the\u00a0standard complex case, a distinguished set of physical states are related to a notion of trace for a certain class of\u00a0bounded operators and, in fact, we show that one can define a suitable space of trace class operators in the non-Archimedean setting, as well.\u00a0\u00a0The statistical interpretation of the (new) theory is completed by suitably defining the observables in p-adic quantum mechanics. We show that the self-adjoint-operator-valued measures (SOVMs) &#8211; a suitable p-adic counterpart of the POVMs associated with a complex Hilbert space &#8211; provide a convenient mathematical tool for this scope.\u00a0The analogies and the differences with respect to the case of standard quantum mechanics\u00a0in a complex Hilbert space are analyzed.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Within the framework of quantum mechanics over a quadratic extension of the non-Archimedean field of p-adic\u00a0numbers, we provide\u00a0a general definition of a quantum state relying on a general algebraic approach and on a p-adic\u00a0model of probability theory. As in the\u00a0standard complex case, a distinguished set of physical states are related to a notion of trace [&hellip;]<\/p>\n","protected":false},"author":2608,"featured_media":0,"template":"","class_list":["post-2116","seminar","type-seminar","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/webs.uab.cat\/giq\/wp-json\/wp\/v2\/seminar\/2116","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\/2608"}],"wp:attachment":[{"href":"https:\/\/webs.uab.cat\/giq\/wp-json\/wp\/v2\/media?parent=2116"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}