[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content
Springer Nature Link
Log in

A remark on transition probability

  • Published:
Letters in Mathematical Physics Aims and scope Submit manuscript

Abstract

Uhlmann's transition probability P(ψ, φ) of two normal states of a von Neumann algebra M, which is the supremum of |(Ψ, Φ)|2 for all possible choices of representative vectors Ψ and Φ of ψ and φ, is shown to be the infimum of (∫d(µψ, e)1/2)2 for the induced measures µω, e(B)=ω(e(B)) (B: Borel set in ℝ, ω=ψ, φ) for all possible projection-valued measures e belonging to M.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Raggio, G.A., ‘Comparison of Uhlmann's transition probability with the one induced by the natural positive cone of von Neumann algebras in standard form’, Lett. Math. Phys. 6, 233–236 (1982).

    MATH  MathSciNet  ADS  Google Scholar 

  2. Uhlmann, A., Rep. Math. Phys. 9, 273 (1976).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  3. Araki, H., Publ. RIMS Kyoto Univ. 8, 335 (1972).

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Research Institute for Mathematical Sciences, Kyoto University, 606, Kyoto, Japan

    Huzihiro Araki

  2. Laboratorium für physikalische Chemie, ETH-Zentrum, CH-8092, Zürich, Switzerland

    Guido A. Raggio

Authors
  1. Huzihiro Araki
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Guido A. Raggio
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Araki, H., Raggio, G.A. A remark on transition probability. Lett Math Phys 6, 237–240 (1982). https://doi.org/10.1007/BF00403278

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00403278

Keywords

Search

Navigation