{"title":"A Note on Geometric Imaginarity","authors":"Tiantian Xia, Jianwei Xu, Ming-Jing Zhao","doi":"10.1007/s10773-024-05866-7","DOIUrl":null,"url":null,"abstract":"<div><p>The imaginarity theory emphasizes the significant role of imaginary component in quantum information. We study the geometric imaginarity which characterizes the imaginarity geometrically. We derive the analytical formulae of the geometric imaginarity for mixed states in qubit systems and X states in high dimensional systems. We also study the evolution of the geometric imaginarity under the action of bit flip channel, phase flip channel and amplitude damping channel. The results show that the geometric imaginarity are contractive under these three quantum channels.</p></div>","PeriodicalId":597,"journal":{"name":"International Journal of Theoretical Physics","volume":"63 12","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2024-12-21","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/s10773-024-05866-7","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
The imaginarity theory emphasizes the significant role of imaginary component in quantum information. We study the geometric imaginarity which characterizes the imaginarity geometrically. We derive the analytical formulae of the geometric imaginarity for mixed states in qubit systems and X states in high dimensional systems. We also study the evolution of the geometric imaginarity under the action of bit flip channel, phase flip channel and amplitude damping channel. The results show that the geometric imaginarity are contractive under these three quantum channels.
意象性理论强调了意象分量在量子信息中的重要作用。我们研究的几何虚像性从几何角度描述了虚像性的特征。我们推导了量子比特系统中混合态和高维系统中 X 态的几何虚像性分析公式。我们还研究了几何想象力在比特翻转通道、相位翻转通道和振幅阻尼通道作用下的演变。结果表明,几何想象力在这三种量子通道作用下都是收缩的。
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.