通过假设检验恢复量子信道的可恢复性

IF 1.3 3区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Letters in Mathematical Physics Pub Date : 2024-02-16 DOI:10.1007/s11005-024-01775-2

Anna Jenčová

{"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}

引用次数: 0

摘要

如果一个量子信道可以在一组输入状态上逆转，那么它对于这组输入状态就是充分的。在近似版本中，输入状态可以在误差范围内恢复，误差以通道下相对熵的减小为界。利用弗伦克尔相对熵的新积分表示法（《量子相对熵的积分公式意味着数据处理不等式》，Quantum 7, 1102 (2023)），我们通过假设检验问题中最优成功概率的保持，等价地，通过 \(L_1\)-distance 的保持，简便地证明了充分量子信道和可恢复性的特征。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Letters in Mathematical Physics 物理-物理：数学物理

CiteScore

2.40

自引率

8.30%

发文量

111

审稿时长

3 months

期刊介绍： 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.