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

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Abstract

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.

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Acknowledgments

This subject was supported by the National Natural Science foundation of China (Nos. 11371012, 11401359, 11471200), the Fundamental Research Fund for the Central Universities (GK201604001), and the Innovation Fund Project for Graduate Program of Shaanxi Normal University (2016CBY005).

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Authors and Affiliations

  1. School of Mathematics and Information Science, Shaanxi Normal University, Xi’an, 710062, China

    Ya-Jing Fan, Huai-Xin Cao, Hui-Xian Meng & Liang Chen

  2. School of Mathematics and Information Science, Beifang University of Nationalities, Yinchuan, 750021, China

    Ya-Jing Fan

  3. Department of Mathematics, Changji College, Changji, 831100, China

    Liang Chen

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  1. Ya-Jing Fan
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  2. Huai-Xin Cao
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  3. Hui-Xian Meng
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Correspondence to Huai-Xin Cao.

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Fan, YJ., Cao, HX., Meng, HX. et al. An uncertainty relation in terms of generalized metric adjusted skew information and correlation measure. Quantum Inf Process 15, 5089–5106 (2016). https://doi.org/10.1007/s11128-016-1419-4

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  • DOI: https://doi.org/10.1007/s11128-016-1419-4

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