Skip to main content
SpringerLink
Log in

Metric Adjusted Skew Information and Metric Adjusted Correlation Measure

  • Conference paper
Nonlinear Mathematics for Uncertainty and its Applications

Part of the book series: Advances in Intelligent and Soft Computing ((AINSC,volume 100))

  • 1857 Accesses

Abstract

We show that a Heisenberg type or a Schrödinger type uncertainty relation for Wigner-Yanase-Dyson skew information proved by Yanagi can hold for an arbitrary quantum Fisher information under some conditions. One of them is a refinement of the result of Gibilisco and Isola.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 259.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 329.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Gibilisco, P., Imparato, D., Isola, T.: Uncertainty principle and quantum Fisher information, II. J. Math. Phys. 48, 72109 (2007)

    Article  MathSciNet  Google Scholar 

  2. Gibilisco, P., Hansen, F., Isola, T.: On a correspondence between regular and non-regular operator monotone functions. Linear Algebra and its Applications 430, 2225–2232 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  3. Gibilisco, P., Isola, T.: On a refinement of Heisenberg uncertainty relation by means of quantum Fisher information. J. Math. Anal. Appl. 375, 270–275 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  4. Hansen, F.: Metric adjusted skew information. Proc. Nat Acad. Sci. 105, 9909–9916 (2008)

    Article  MATH  Google Scholar 

  5. Kubo, F., Ando, T.: Means of positive linear operators. Math. Ann. 246, 205–224 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  6. Luo, S.: Heisenberg uncertainty relation for mixed states. Phys. Rev. A 72, 42110 (2005)

    Article  Google Scholar 

  7. Petz, D.: Monotone metrics on matrix spaces. Linear Algebra and its Applications 244, 81–96 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  8. Petz, D., Hasegawa, H.: On the Riemannian metric of α-entropies of density matrices. Lett. Math. Phys. 38, 221–225 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  9. Wigner, E.P., Yanase, M.M.: Information content of distribution. Proc. Nat. Acad. Sci. 49, 910–918 (1963)

    Article  MathSciNet  MATH  Google Scholar 

  10. Yanagi, K.: Uncertainty relation on Wigner-Yanase-Dyson skew information. J. Math. Anal. Appl. 365, 12–18 (2010)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Division of Applied Mathematical Science, Graduate School of Science and Engineering, Yamaguchi University, 2-16-1, Tokiwadai, Ube, 755-8611, Japan

    Kenjiro Yanagi

  2. Department of Computer Science and System Analysis, College of Humanities and Sciences, Nihon University, 3-25-40, Sakurajyousui, Setagaya-ku, Tokyo, 156-8550, Japan

    Shigeru Furuichi

Authors
  1. Kenjiro Yanagi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shigeru Furuichi
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. College of Applied Sciences, Beijing University of Technology, 100 Pingleyuan, 100124, Chaoyang District, Beijing, P.R. China

    Shoumei Li , Xia Wang  & Li Guan ,  & 

  2. Department of Systems Design and Informatics, Kyushu Institute of Technology, 680-4, Kawazu, 820-8502, lizuka, Japan

    Yoshiaki Okazaki

  3. Department of Mathematics, Shinshu University, 4-17-1 Wakasato, 380-8553, Nagano, Japan

    Jun Kawabe

  4. Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, 4259-G3-47, Nagatsuta, Midori-ku, 226-8502, Yokohama, Japan

    Toshiaki Murofushi

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Yanagi, K., Furuichi, S. (2011). Metric Adjusted Skew Information and Metric Adjusted Correlation Measure. In: Li, S., Wang, X., Okazaki, Y., Kawabe, J., Murofushi, T., Guan, L. (eds) Nonlinear Mathematics for Uncertainty and its Applications. Advances in Intelligent and Soft Computing, vol 100. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22833-9_38

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-22833-9_38

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22832-2

  • Online ISBN: 978-3-642-22833-9

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation