{"id":1124,"date":"2018-01-08T16:16:50","date_gmt":"2018-01-08T14:16:50","guid":{"rendered":"https:\/\/webs.uab.cat\/giq\/seminar\/lower-bounds-on-the-quantum-fisher-information-based-on-the-variance-and-various-types-of-entropies\/"},"modified":"2018-01-08T16:16:50","modified_gmt":"2018-01-08T14:16:50","slug":"lower-bounds-on-the-quantum-fisher-information-based-on-the-variance-and-various-types-of-entropies","status":"publish","type":"seminar","link":"https:\/\/webs.uab.cat\/giq\/seminar\/lower-bounds-on-the-quantum-fisher-information-based-on-the-variance-and-various-types-of-entropies\/","title":{"rendered":"Lower bounds on the quantum Fisher information based on the variance and various types of entropies"},"content":{"rendered":"<p>We examine important properties of the difference between the variance<br \/>\nand the quantum Fisher information over four, i.e., (\u0394A)2\u2212FQ[\u03f1,A]\/4.<br \/>\nWe find that it is equal to a generalized variance defined in Petz [J.<br \/>\nPhys. A 35, 929 (2002)] and Gibilisco, Hiai, and Petz [IEEE Trans.<br \/>\nInf. Theory 55, 439 (2009)]. We present an upper bound on this<br \/>\nquantity that is proportional to the linear entropy. As expected, our<br \/>\nrelations show that for states that are close to being pure, the<br \/>\nquantum Fisher information over four is close to the variance. We also<br \/>\nobtain the variance and the quantum Fisher averaged over all Hermitian<br \/>\noperators, and examine their relation to the von Neumann entropy.<\/p>\n<p>[1] G. <span class=\"il\">Toth<\/span>, arxiv:1701.07461.<\/p>\n<div class=\"yj6qo\">&nbsp;<\/div>\n<div class=\"adL\">&nbsp;<\/div>\n","protected":false},"excerpt":{"rendered":"<p>We examine important properties of the difference between the variance and the quantum Fisher information over four, i.e., (\u0394A)2\u2212FQ[\u03f1,A]\/4. We find that it is equal to a generalized variance defined in Petz [J. Phys. A 35, 929 (2002)] and Gibilisco, Hiai, and Petz [IEEE Trans. Inf. Theory 55, 439 (2009)]. We present an upper bound [&hellip;]<\/p>\n","protected":false},"author":20,"featured_media":0,"template":"","class_list":["post-1124","seminar","type-seminar","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/webs.uab.cat\/giq\/wp-json\/wp\/v2\/seminar\/1124","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=1124"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}