Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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SCHRÖDINGER UNCERTAINTY RELATION FOR THE MONOTONE TRIPLE SKEW INFORMATION

  • Ko, Chul Ki (University College Yonsei University) ;
  • Yoo, Hyun Jae (Department of Applied Mathematics Hankyong National University)
  • Received : 2016.01.27
  • Published : 2017.01.31
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Abstract

We get a $Schr{\ddot{o}}dinger$ uncertainty relation for the monotone triple skew information which was introduced by Yanagi and Kajihara. This information extends the monotone pair skew information as well as Wigner-Yanase-Dyson skew information.

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References

  1. L. Cai and S. Luo, On convexity of generalized Wigner-Yanase-Dyson information, Lett. Math. Phys. 83 (2008), no. 3, 253-264. https://doi.org/10.1007/s11005-008-0222-2
  2. S. Furuichi, Inequalities for Tsallis relative entropy and generalized skew information, Linear Multilinear Algebra 59 (2011), no. 10, 1143-1158. https://doi.org/10.1080/03081087.2011.574624
  3. S. Furuich and K. Yanagi, Schrdinger uncertainty relation, Wigner-Yanase-Dyson skew information and metric adjusted correlation measure, J. Math. Anal. Appl. 388 (2012), no. 2, 1147-1156. https://doi.org/10.1016/j.jmaa.2011.10.061
  4. C. K. Ko and H. J. Yoo, Uncertainty relation associated with a monotone pair skew information, J. Math. Anal. Appl. 383 (2011), no. 1, 208-214. https://doi.org/10.1016/j.jmaa.2011.05.014
  5. C. K. Ko and H. J. Yoo, Schrodinger uncertainty relation and convexity for the monotone pair skew information, Tohoku Math. J. 66 (2014), no. 1, 107-117. https://doi.org/10.2748/tmj/1396875665
  6. E. H. Lieb, Convex trace functions and the Wigner-Yanase-Dyson conjecture, Adv. Math. 11 (1973), 267-288. https://doi.org/10.1016/0001-8708(73)90011-X
  7. E. P. Wigner and M. M. Yanase, Information content of distribution, Proc. Nat. Acad. Sci. U.S.A. 49 (1963), 910-918. https://doi.org/10.1073/pnas.49.6.910
  8. K. Yanagi, Uncertainty relation on generalized Wigner-Yanase-Dyson skew information, Linear Algebra Appl. 433 (2010), no. 8-10, 1524-1532. https://doi.org/10.1016/j.laa.2010.05.024
  9. K. Yanagi, Uncertainty relation on Wigner-Yanase-Dyson skew information, J. Math. Anal. Appl. 365 (2010), no. 1, 12-18. https://doi.org/10.1016/j.jmaa.2009.09.060
  10. K. Yanagi and S. Kajihara, Generalized uncertainty relation associated with a monotone or anti-monotone pair skew information, Research and communications in Mathematics and Mathematical Sciences 1, Issue 1 (2012), 1-18.