Skip to main content
SpringerLink
Log in

Towards Quantum ɛ—Entropy and Validity of Quantum Information

  • Chapter
Maximum Entropy and Bayesian Methods

Part of the book series: Fundamental Theories of Physics ((FTPH,volume 53))

  • 416 Accesses

Abstract

The Bayesian method in quantum signal processing was initiated by C W Helstrom and developed in quantum detection [1], estimation [2, 3] and hypothesis testing [4] theory. The aim of this theory was to find an optimal quantum measurement, minimizing a cost function of quantum state estimation under given probabilities of possible states. The usefulness of entropy restrictions for the finding of the quantum estimation was shown in [2], where a quantum regression problem was solved under the condition of fixed entropy of quantum measurement.

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

References

  1. C.W. Helstrom, Quantum detection and estimation theory, Academic Press, 1976.

    Google Scholar 

  2. V. P. Belavkin, Optimal quantum randomized filtration, Problems of Control and Inform Theory, 3, 25, 1974.

    MathSciNet  Google Scholar 

  3. A. S. Holevo, Probabilistic aspects of quantum theory, Kluwer Publisher, 1980.

    Google Scholar 

  4. V. P. Belavkin, Optimal multiple quantum hypothesis testing, Stochastics, 3, 40, 1975.

    MathSciNet  Google Scholar 

  5. R. L. Stratonovich, Theory of information, Soy Radio, Moscow, 1976.

    Google Scholar 

  6. V. P. Belavkin, Optimal quantization of random vectors, Isvestia A N USSR, Techn Kibernetika, 1, 20, 1970.

    Google Scholar 

  7. F. Hiai, Ohya M, Tsukada M, Sufficiency, KMS condition and relative entropy in von Neumann algebras, Pacific J Math, 93, 99, 1981.

    Article  MathSciNet  Google Scholar 

  8. V. P. Belavkin, Staszewski P, C*-algebraic generalization of relative entropy and entropy, Ann Inst H Poincaré, Sect A 37, 51, 1982.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Nottingham, Nottingham, NG7 2RD, UK

    V. P. Belavkin

Authors
  1. V. P. Belavkin
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Groupe Problèmes Inverses, Laboratoire des Signaux et Systèmes (CNRS-ESE-UPS), 91192, Gif-sur-Yvette Cedex, France

    Ali Mohammad-Djafari  & Guy Demoment  & 

Rights and permissions

Reprints and permissions

Copyright information

© 1993 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Belavkin, V.P. (1993). Towards Quantum ɛ—Entropy and Validity of Quantum Information. In: Mohammad-Djafari, A., Demoment, G. (eds) Maximum Entropy and Bayesian Methods. Fundamental Theories of Physics, vol 53. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2217-9_21

Download citation

  • DOI: https://doi.org/10.1007/978-94-017-2217-9_21

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4272-9

  • Online ISBN: 978-94-017-2217-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation