An uncertainty relation in terms of generalized metric adjusted skew information and correlation measure

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• 作者：Ya-Jing Fan ; Huai-Xin Cao ; Hui-Xian Meng ; Liang Chen
• 关键词：Uncertainty relation ; Generalized metric adjusted skew information ; Generalized metric adjusted correlation measure ; Wigner–Yanase skew information ; Wigner–Yanase–Dyson skew information
• 刊名：Quantum Information Processing
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：15
• 期：12
• 页码：5089-5106
• 全文大小：
• 刊物类别：Physics and Astronomy
• 刊物主题：Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics;
• 出版者：Springer US
• ISSN：1573-1332
• 卷排序：15

文摘

The uncertainty principle in quantum mechanics is a fundamental relation with different forms, including Heisenberg’s uncertainty relation and Schrödinger’s uncertainty relation. In this paper, we prove a Schrödinger-type uncertainty relation in terms of generalized metric adjusted skew information and correlation measure by using operator monotone functions, which reads, $$\begin{aligned} U_\rho ^{(g,f)}(A)U_\rho ^{(g,f)}(B)\ge \frac{f(0)^2l}{k}\left| \mathrm {Corr}_\rho ^{s(g,f)}(A,B)\right| ^2 \end{aligned}$$for some operator monotone functions f and g, all n-dimensional observables A, B and a non-singular density matrix \(\rho \). As applications, we derive some new uncertainty relations for Wigner–Yanase skew information and Wigner–Yanase–Dyson skew information.KeywordsUncertainty relationGeneralized metric adjusted skew informationGeneralized metric adjusted correlation measureWigner–Yanase skew informationWigner–Yanase–Dyson skew informationReferences1.Heisenberg, W.: Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik. Z. Phys. A 43, 172–198 (1927)CrossRefGoogle Scholar2.Schrödinger, E.: About Heisenberg uncertainty relation. Proc. Prussian Acad. Sci. Phys. Math. Sect. 19, 296–303 (1930)Google Scholar3.Luo, S.: Heisenberg uncertainty relation for mixed states. Phys. Rev. A 72, 042110 (2005)ADSCrossRefGoogle Scholar4.Furuichi, S.: Schrödinger uncertainty relation with Wigner-Yanase skew information. Phys. Rev. A 82, 034101 (2010)ADSCrossRefGoogle Scholar5.Yanagi, K.: Uncertainty relation on Wigner-Yanase-Dyson skew information. J. Math. Anal. 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Astron. 59, 630301 (2016)CrossRefGoogle ScholarCopyright information© Springer Science+Business Media New York 2016Authors and AffiliationsYa-Jing Fan12Huai-Xin Cao1Email authorHui-Xian Meng1Liang Chen131.School of Mathematics and Information ScienceShaanxi Normal UniversityXi’anChina2.School of Mathematics and Information ScienceBeifang University of NationalitiesYinchuanChina3.Department of MathematicsChangji CollegeChangjiChina About this article CrossMark Publisher Name Springer US Print ISSN 1570-0755 Online ISSN 1573-1332 About this journal Reprints and Permissions Article actions .buybox { margin: 16px 0 0; position: relative; } .buybox { font-family: Source Sans Pro, Helvetica, Arial, sans-serif; font-size: 14px; font-size: .875rem; } .buybox { zoom: 1; } .buybox:after, .buybox:before { content: ''; display: table; } .buybox:after { clear: both; } /*---------------------------------*/ .buybox .buybox__header { border: 1px solid #b3b3b3; border-bottom: 0; padding: 8px 12px; position: relative; 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