{"id":1116,"date":"2017-09-17T19:41:50","date_gmt":"2017-09-17T17:41:50","guid":{"rendered":"https:\/\/webs.uab.cat\/giq\/seminar\/distinguishing-generic-quantum-states\/"},"modified":"2017-09-17T19:41:50","modified_gmt":"2017-09-17T17:41:50","slug":"distinguishing-generic-quantum-states","status":"publish","type":"seminar","link":"https:\/\/webs.uab.cat\/giq\/seminar\/distinguishing-generic-quantum-states\/","title":{"rendered":"Distinguishing generic quantum states"},"content":{"rendered":"<p>Properties of random mixed states of dimension $N$<br \/>\ndistributed uniformly with respect to the Hilbert-Schmidt measure are<br \/>\ninvestigated. We show that for large $N$, due to the concentration of measure<br \/>\nphenomenon, the trace distance between two random states tends to a fixed&nbsp; number&nbsp;<br \/>\n$1\/4+1\/\\pi$, which yields the Helstrom bound on their distinguishability. To<br \/>\narrive at this result we apply free random calculus and derive the symmetrized Marchenko&#8211;Pastur&nbsp;<br \/>\ndistribution. Asymptotic value for the root fidelity between two random states,&nbsp;<br \/>\n$\\sqrt{F}=3\/4$, can serve as a universal reference value<br \/>\nfor further theoretical and experimental studies.<br \/>\nAnalogous results for quantum relative entropy and<br \/>\nChernoff quantity provide other bounds on the distinguishablity of both states<br \/>\nin a multiple measurement setup due to the quantum Sanov theorem. Entanglement<br \/>\nof a generic mixed state of a bi&#8211;partite system is estimated.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Properties of random mixed states of dimension $N$ distributed uniformly with respect to the Hilbert-Schmidt measure are investigated. We show that for large $N$, due to the concentration of measure phenomenon, the trace distance between two random states tends to a fixed&nbsp; number&nbsp; $1\/4+1\/\\pi$, which yields the Helstrom bound on their distinguishability. To arrive at [&hellip;]<\/p>\n","protected":false},"author":20,"featured_media":0,"template":"","class_list":["post-1116","seminar","type-seminar","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/webs.uab.cat\/giq\/wp-json\/wp\/v2\/seminar\/1116","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=1116"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}