{"title":"通过假设检验恢复量子信道的可恢复性","authors":"Anna Jenčová","doi":"10.1007/s11005-024-01775-2","DOIUrl":null,"url":null,"abstract":"<div><p>A quantum channel is sufficient with respect to a set of input states if it can be reversed on this set. In the approximate version, the input states can be recovered within an error bounded by the decrease of the relative entropy under the channel. Using a new integral representation of the relative entropy in Frenkel (Integral formula for quantum relative entropy implies data processing inequality, Quantum <b>7</b>, 1102 (2023)), we present an easy proof of a characterization of sufficient quantum channels and recoverability by preservation of optimal success probabilities in hypothesis testing problems, equivalently, by preservation of <span>\\(L_1\\)</span>-distance.\n</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-024-01775-2.pdf","citationCount":"0","resultStr":"{\"title\":\"Recoverability of quantum channels via hypothesis testing\",\"authors\":\"Anna Jenčová\",\"doi\":\"10.1007/s11005-024-01775-2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>A quantum channel is sufficient with respect to a set of input states if it can be reversed on this set. In the approximate version, the input states can be recovered within an error bounded by the decrease of the relative entropy under the channel. Using a new integral representation of the relative entropy in Frenkel (Integral formula for quantum relative entropy implies data processing inequality, Quantum <b>7</b>, 1102 (2023)), we present an easy proof of a characterization of sufficient quantum channels and recoverability by preservation of optimal success probabilities in hypothesis testing problems, equivalently, by preservation of <span>\\\\(L_1\\\\)</span>-distance.\\n</p></div>\",\"PeriodicalId\":685,\"journal\":{\"name\":\"Letters in Mathematical Physics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2024-02-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s11005-024-01775-2.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Letters in Mathematical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s11005-024-01775-2\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Letters in Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s11005-024-01775-2","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
Recoverability of quantum channels via hypothesis testing
A quantum channel is sufficient with respect to a set of input states if it can be reversed on this set. In the approximate version, the input states can be recovered within an error bounded by the decrease of the relative entropy under the channel. Using a new integral representation of the relative entropy in Frenkel (Integral formula for quantum relative entropy implies data processing inequality, Quantum 7, 1102 (2023)), we present an easy proof of a characterization of sufficient quantum channels and recoverability by preservation of optimal success probabilities in hypothesis testing problems, equivalently, by preservation of \(L_1\)-distance.
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The aim of Letters in Mathematical Physics is to attract the community''s attention on important and original developments in the area of mathematical physics and contemporary theoretical physics. The journal publishes letters and longer research articles, occasionally also articles containing topical reviews. We are committed to both fast publication and careful refereeing. In addition, the journal offers important contributions to modern mathematics in fields which have a potential physical application, and important developments in theoretical physics which have potential mathematical impact.
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