{"title":"相干理论中的量子态变换","authors":"Jie Cui, Ming-Jing Zhao","doi":"10.1007/s10773-024-05742-4","DOIUrl":null,"url":null,"abstract":"<p>We study the transformation between quantum states under incoherent operations and unitary incoherent operations. In high dimensional systems, we show any two pure states can be transformed into each other under incoherent operations if and only if they can be transformed into each other under unitary incoherent operations. For mixed states, we show any two incoherent states can be transformed into each other under incoherent operations. Furthermore, we show any incoherent states can be transformed by any mixed states under incoherent operations. In qubit systems, we prove the necessary and sufficient condition for the transformation between any two mixed states by incoherent operations alternatively and obtain the corresponding incoherent operations. Moreover we prove any two mixed qubit states with nonzero coherence can be transformed into each other under incoherent operations if and only if they can be transformed into each other under unitary incoherent operations.</p>","PeriodicalId":597,"journal":{"name":"International Journal of Theoretical Physics","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Transformation of Quantum States in Coherence Theory\",\"authors\":\"Jie Cui, Ming-Jing Zhao\",\"doi\":\"10.1007/s10773-024-05742-4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We study the transformation between quantum states under incoherent operations and unitary incoherent operations. In high dimensional systems, we show any two pure states can be transformed into each other under incoherent operations if and only if they can be transformed into each other under unitary incoherent operations. For mixed states, we show any two incoherent states can be transformed into each other under incoherent operations. Furthermore, we show any incoherent states can be transformed by any mixed states under incoherent operations. In qubit systems, we prove the necessary and sufficient condition for the transformation between any two mixed states by incoherent operations alternatively and obtain the corresponding incoherent operations. Moreover we prove any two mixed qubit states with nonzero coherence can be transformed into each other under incoherent operations if and only if they can be transformed into each other under unitary incoherent operations.</p>\",\"PeriodicalId\":597,\"journal\":{\"name\":\"International Journal of Theoretical Physics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2024-08-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Theoretical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1007/s10773-024-05742-4\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"PHYSICS, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Theoretical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1007/s10773-024-05742-4","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
The Transformation of Quantum States in Coherence Theory
We study the transformation between quantum states under incoherent operations and unitary incoherent operations. In high dimensional systems, we show any two pure states can be transformed into each other under incoherent operations if and only if they can be transformed into each other under unitary incoherent operations. For mixed states, we show any two incoherent states can be transformed into each other under incoherent operations. Furthermore, we show any incoherent states can be transformed by any mixed states under incoherent operations. In qubit systems, we prove the necessary and sufficient condition for the transformation between any two mixed states by incoherent operations alternatively and obtain the corresponding incoherent operations. Moreover we prove any two mixed qubit states with nonzero coherence can be transformed into each other under incoherent operations if and only if they can be transformed into each other under unitary incoherent operations.
期刊介绍:
International Journal of Theoretical Physics publishes original research and reviews in theoretical physics and neighboring fields. Dedicated to the unification of the latest physics research, this journal seeks to map the direction of future research by original work in traditional physics like general relativity, quantum theory with relativistic quantum field theory,as used in particle physics, and by fresh inquiry into quantum measurement theory, and other similarly fundamental areas, e.g. quantum geometry and quantum logic, etc.