{"id":962,"date":"2013-08-19T11:57:48","date_gmt":"2013-08-19T09:57:48","guid":{"rendered":"https:\/\/webs.uab.cat\/giq\/seminar\/tba-0-2\/"},"modified":"2013-08-19T11:57:48","modified_gmt":"2013-08-19T09:57:48","slug":"tba-0-2","status":"publish","type":"seminar","link":"https:\/\/webs.uab.cat\/giq\/seminar\/tba-0-2\/","title":{"rendered":"Purifications of multipartite states: limitations and constructive methods"},"content":{"rendered":"<p>We analyze the description of quantum many-body mixed states using matrix product states and operators. We consider two descriptions: (i) as a matrix product density operator of bond dimension D, and (ii) as a purification that is written as a matrix product state of bond dimension D&#8217;. We show that these descriptions are inequivalent in the sense that D&#8217; cannot be upper bounded by D only. We then provide two methods to obtain (ii) out of (i). The sum of squares (sos) polynomial method upper bounds D&#8217; by D to the power of the number of different eigenvalues. Its approximate version is formulated as a Semidefinite Program, and it gives approximate purifications whose D&#8217; only depends on D. The eigenbasis method upper bounds D&#8217; by D times the number of eigenvalues, and its approximate version is very efficient for exponentially decaying distributions. Our results imply that a description of mixed states which is both efficient and locally positive semidefinite does not exist, but that good approximations do.<\/p>\n<p>Joint work with N. Schuch, D. P\u00e9rez-Garc\u00eda, and J. I. Cirac.<\/p>\n<div class=\"yj6qo ajU\">\n<div id=\":3p8\" class=\"ajR\" data-tooltip=\"Muestra el contenido reducido\"><img decoding=\"async\" class=\"ajT\" src=\"https:\/\/mail.google.com\/mail\/u\/0\/images\/cleardot.gif\" alt=\"\" \/><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>We analyze the description of quantum many-body mixed states using matrix product states and operators. We consider two descriptions: (i) as a matrix product density operator of bond dimension D, and (ii) as a purification that is written as a matrix product state of bond dimension D&#8217;. We show that these descriptions are inequivalent in [&hellip;]<\/p>\n","protected":false},"author":20,"featured_media":0,"template":"","class_list":["post-962","seminar","type-seminar","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/webs.uab.cat\/giq\/wp-json\/wp\/v2\/seminar\/962","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=962"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}