{"title":"Perfect NOT and conjugate transformations","authors":"Fengli Yan, Ting Gao","doi":"10.1007/s43673-022-00038-3","DOIUrl":null,"url":null,"abstract":"<div><p>We obtain the perfect NOT transformation criteria, two necessary and sufficient conditions for realizing a perfect NOT transformation on a quantum state set <i>S</i> of a qubit. Furthermore, we discuss a probabilistic perfect NOT transformation when there is no perfect NOT transformation on a state set <i>S</i>. We also generalize the perfect NOT transformation to the conjugate transformation in the multi-level quantum system and a lower bound of the best possible efficiencies attained by a probabilistic perfect conjugate transformation are obtained.</p></div>","PeriodicalId":100007,"journal":{"name":"AAPPS Bulletin","volume":"32 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2022-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43673-022-00038-3.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"AAPPS Bulletin","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s43673-022-00038-3","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We obtain the perfect NOT transformation criteria, two necessary and sufficient conditions for realizing a perfect NOT transformation on a quantum state set S of a qubit. Furthermore, we discuss a probabilistic perfect NOT transformation when there is no perfect NOT transformation on a state set S. We also generalize the perfect NOT transformation to the conjugate transformation in the multi-level quantum system and a lower bound of the best possible efficiencies attained by a probabilistic perfect conjugate transformation are obtained.
我们获得了完美 NOT 变换标准，即在量子比特的量子态集 S 上实现完美 NOT 变换的两个必要条件和充分条件。此外，我们还讨论了当状态集 S 上不存在完美 NOT 变换时的概率完美 NOT 变换。我们还将完美 NOT 变换推广到多级量子系统中的共轭变换，并获得了概率完美共轭变换所能达到的最佳效率下限。
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