Two generalized Wigner–Yanase skew information and their uncertainty relations

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• 作者：Zheng-Li Chen ; Li-Li Liang ; Hao-Jing Li ; Wen-Hua Wang
• 关键词：Generalized Wigner–Yanase skew information ; Uncertainty relation ; Wigner–Yanase skew information ; Density operator ; Symmetrized commutator
• 刊名：Quantum Information Processing
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：15
• 期：12
• 页码：5107-5118
• 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

In this paper, we first define two generalized Wigner–Yanase skew information \(|K_{\rho ,\alpha }|(A)\) and \(|L_{\rho ,\alpha }|(A)\) for any non-Hermitian Hilbert–Schmidt operator A and a density operator \(\rho \) on a Hilbert space H and discuss some properties of them, respectively. We also introduce two related quantities \(|S_{\rho ,\alpha }|(A)\) and \(|T_{\rho ,\alpha }|(A)\). Then, we establish two uncertainty relations in terms of \(|W_{\rho ,\alpha }|(A)\) and \(|\widetilde{W}_{\rho ,\alpha }|(A)\), which read $$\begin{aligned}&|W_{\rho ,\alpha }|(A)|W_{\rho ,\alpha }|(B)\ge \frac{1}{4}\left| \mathrm {tr}\left( \left[ \frac{\rho ^{\alpha }+\rho ^{1-\alpha }}{2} \right] ^{2}[A,B]^{0}\right) \right| ^{2},\\&\sqrt{|\widetilde{W}_{\rho ,\alpha }|(A)| \widetilde{W}_{\rho ,\alpha }|(B)}\ge \frac{1}{4} \left| \mathrm {tr}\left( \rho ^{2\alpha }[A,B]^{0}\right) \mathrm {tr} \left( \rho ^{2(1-\alpha )}[A,B]^{0}\right) \right| . \end{aligned}$$KeywordsGeneralized Wigner–Yanase skew informationUncertainty relationWigner–Yanase skew informationDensity operatorSymmetrized commutatorReferences1.Wigner, E.P., Yanase, M.M.: Information contents of distributions. Proc. Natl. Acad. Sci. USA 49, 910–918 (1963)ADSMathSciNetCrossRefMATHGoogle Scholar2.Streater, R.F.: Classical and quantum probability. J. Math. 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(2016). doi:10.1007/s11128-016-1354-4 MathSciNetMATHGoogle ScholarCopyright information© Springer Science+Business Media New York 2016Authors and AffiliationsZheng-Li Chen1Email authorLi-Li Liang1Hao-Jing Li1Wen-Hua Wang11.School of Mathematics and Information ScienceShaanxi Normal UniversityXi’anChina 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; background-color: #f2f2f2; } .buybox__header .buybox__login { font-family: Source Sans Pro, Helvetica, Arial, sans-serif; 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