{"title":"Quantum Rényi Entropy with Localization Characteristics","authors":"Qi Han, Shuai Wang, Lijie Gou, Rong Zhang","doi":"10.1007/s10773-024-05816-3","DOIUrl":null,"url":null,"abstract":"<div><p>This paper presents a localized treatment of quantum Rényi entropy. Specifically, based on the localized characteristics of Local Quantum Bernoulli Noises (LQBNs), a new definition of quantum Rényi entropy, that is, quantum Rényi entropy with localization characteristics, is given through the local density operator constructed by local conservative operators <span>\\(l_{k}^{\\circ } \\)</span>. We also verify that this new definition possesses properties such as unitary invariance, additivity, monotonicity, and weak subadditivity. Furthermore, through the monotonicity of the local quantum Rényi entropy, we derive the local quantum Rényi minimum entropy and the local quantum Rényi maximum entropy. The local quantum Rényi entropy can be used to study quantum entanglement and coherence. For instance, in the contexts of quantum phase transitions and quantum state transmission, the local quantum Rényi entropy can provide important insights into the flow of information and interactions within quantum systems.</p></div>","PeriodicalId":597,"journal":{"name":"International Journal of Theoretical Physics","volume":"63 11","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2024-10-30","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://link.springer.com/article/10.1007/s10773-024-05816-3","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}
引用次数: 0
Abstract
This paper presents a localized treatment of quantum Rényi entropy. Specifically, based on the localized characteristics of Local Quantum Bernoulli Noises (LQBNs), a new definition of quantum Rényi entropy, that is, quantum Rényi entropy with localization characteristics, is given through the local density operator constructed by local conservative operators \(l_{k}^{\circ } \). We also verify that this new definition possesses properties such as unitary invariance, additivity, monotonicity, and weak subadditivity. Furthermore, through the monotonicity of the local quantum Rényi entropy, we derive the local quantum Rényi minimum entropy and the local quantum Rényi maximum entropy. The local quantum Rényi entropy can be used to study quantum entanglement and coherence. For instance, in the contexts of quantum phase transitions and quantum state transmission, the local quantum Rényi entropy can provide important insights into the flow of information and interactions within quantum systems.
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.
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