{"id":1198,"date":"2020-02-04T11:42:22","date_gmt":"2020-02-04T09:42:22","guid":{"rendered":"https:\/\/webs.uab.cat\/giq\/seminar\/reading-club-a-resource-approach-to-the-steins-lemma-for-channel-discrimination\/"},"modified":"2020-02-04T11:42:22","modified_gmt":"2020-02-04T09:42:22","slug":"reading-club-a-resource-approach-to-the-steins-lemma-for-channel-discrimination","status":"publish","type":"seminar","link":"https:\/\/webs.uab.cat\/giq\/seminar\/reading-club-a-resource-approach-to-the-steins-lemma-for-channel-discrimination\/","title":{"rendered":"Reading Club: A resource approach to the Stein&#8217;s Lemma for channel discrimination"},"content":{"rendered":"<p class=\"rtejustify\">The quantum Stein&#8217;s Lemma gives the asymptotic error for&nbsp;simple i.i.d. hypothesis testing between two states, where the type-I&nbsp; error is bounded away from 1, and the type-II error is exponentially&nbsp;small. The exponent is given by the quantum relative entropy&nbsp;between&nbsp;the states. The corresponding question for quantum&nbsp;channels (cptp maps) a priori&nbsp;has two answers, depending on whether we allow adaptive strategies&nbsp;to discriminate the channels or not. In a series of recent papers,&nbsp;Berta et al. (1808.01498), Wang\/Wilde (1907.06306) and Fang et al. (1909.05826)&nbsp;have solved both questions and shown that the answers are the&nbsp;same: the Stein exponent for asymmetric channel hypothesis testing,&nbsp;i.e. discriminating&nbsp;between&nbsp;n copies of a channel N and n copies of&nbsp;a channel M, using adaptive strategies is given by the&nbsp;amortized&nbsp;channel divergence, and this quantity equals the regularized plain&nbsp;channel divergence, which is the optimal exponent for parallel strategies.&nbsp;The first part relies on a beautiful resource theory, going back to&nbsp;Matsumoto (1010.1030) in the state setting, where the objects are&nbsp;_pairs_ of quantum channels. The second part is surprisingly not&nbsp;operational, but based on chain rule relations for the relative entropy.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The quantum Stein&#8217;s Lemma gives the asymptotic error for&nbsp;simple i.i.d. hypothesis testing between two states, where the type-I&nbsp; error is bounded away from 1, and the type-II error is exponentially&nbsp;small. The exponent is given by the quantum relative entropy&nbsp;between&nbsp;the states. The corresponding question for quantum&nbsp;channels (cptp maps) a priori&nbsp;has two answers, depending on whether we [&hellip;]<\/p>\n","protected":false},"author":20,"featured_media":0,"template":"","class_list":["post-1198","seminar","type-seminar","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/webs.uab.cat\/giq\/wp-json\/wp\/v2\/seminar\/1198","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=1198"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}