{"id":1229,"date":"2021-02-17T17:35:32","date_gmt":"2021-02-17T15:35:32","guid":{"rendered":"https:\/\/webs.uab.cat\/giq\/seminar\/the-quantum-marginal-problem\/"},"modified":"2021-02-17T17:35:32","modified_gmt":"2021-02-17T15:35:32","slug":"the-quantum-marginal-problem","status":"publish","type":"seminar","link":"https:\/\/webs.uab.cat\/giq\/seminar\/the-quantum-marginal-problem\/","title":{"rendered":"The quantum marginal problem"},"content":{"rendered":"<p><font size=\"2\"><span>The quantum marginal problem<\/p>\n<p>Clarifying the relation between the whole and its parts<br \/>\nis crucial for many problems in science. In quantum<br \/>\nmechanics, this question manifests itself in the quantum<br \/>\nmarginal problem, which asks whether there is a global pure<br \/>\nquantum state for some given marginals. This problem arises<br \/>\nin many contexts, ranging from quantum chemistry to entanglement<br \/>\ntheory and quantum error correcting codes.<\/p>\n<p>In this talk I will first present an introduction into<br \/>\nthis problem and its applications. Then, I will discuss<br \/>\nthe problem of absolutely maximally entangled states as<br \/>\na special instance. Finally, I will prove a correspondence<br \/>\nof the marginal problem to the separability problem. Based<br \/>\non this, I describe a sequence of semidefinite programs<br \/>\nwhich can decide whether some given marginals are compatible<br \/>\nwith some pure global quantum state. As an application, I<br \/>\nprove that the existence of multi-particle absolutely<br \/>\nmaximally entangled states for a given dimension is<br \/>\nequivalent to the separability of an explicitly given<br \/>\ntwo-party quantum state.<\/p>\n<p>&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;-<br \/>\nReference:<br \/>\nX.-D. Yu, T. Simnacher, N. Wyderka, H. C. Nguyen, O. G\u00fchne,<br \/>\nA complete hierarchy for the pure state marginal problem in<br \/>\nquantum mechanics<br \/>\nNature Communications 12, 1012 (2021).<\/span><\/font><\/p>\n","protected":false},"excerpt":{"rendered":"<p>The quantum marginal problem Clarifying the relation between the whole and its parts is crucial for many problems in science. In quantum mechanics, this question manifests itself in the quantum marginal problem, which asks whether there is a global pure quantum state for some given marginals. This problem arises in many contexts, ranging from quantum [&hellip;]<\/p>\n","protected":false},"author":20,"featured_media":0,"template":"","class_list":["post-1229","seminar","type-seminar","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/webs.uab.cat\/giq\/wp-json\/wp\/v2\/seminar\/1229","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=1229"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}