Statistical Inference by Minimal Bures Distance

  • Jean-Paul Marchand


We have developed, over the past years, a general theory of statistical inference in quantum mechanics1-6 that has now reached a stage in which a presentation based on first principles seems appropriate.


Relative Entropy Statistical INFERENcE Partial Measurement Insufficient Reason Maximum Entropy State 
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References and Notes

  1. 1.
    J.-P. Marchand, Found. Phys. 7, 35 (1977).CrossRefGoogle Scholar
  2. 2.
    S. Gudder, J.-P. Marchand, and W. Wyss, J. Math. Phys. 20, 1963 (1979).CrossRefGoogle Scholar
  3. 3.
    J.-P. Marchand and W. Wyss, J. Stat. Phys. 16, 349 (1977).CrossRefGoogle Scholar
  4. 4.
    R. Benoist and J.-P. Marchand, Lett. Math. Phys. 3, 93 (1979).CrossRefGoogle Scholar
  5. 5.
    R. Benoist, J.-P. Marchand, and W. Yourgrau, Found. Phys. 7, 827 (1977).CrossRefGoogle Scholar
  6. 6.
    R. Benoist, J.-P. Marchand, and W. Wyss, Lett. Math. Phys. 3, 169 (1979).CrossRefGoogle Scholar
  7. 7.
    S. Sakai, Bull. AMS 71, 149 (1965).CrossRefGoogle Scholar
  8. 8.
    D. Bures, Trans. AMS 135, 199 (1969).Google Scholar
  9. 9.
    A. Uhlmann, Rep. Math. Phys. 9, 273, (1976).CrossRefGoogle Scholar
  10. 10.
    H. Araki, RIMS, Kyoto Univ. 8, 335 (1972).CrossRefGoogle Scholar
  11. 11.
    S. Gudder, Intl. Journ. Theoret. Phys. 20 383 (1981).CrossRefGoogle Scholar
  12. 12.
    R. Benoist, Thesis, Univ. of Denver (1978).Google Scholar
  13. 13.
    S. Gudder, Rep. Math. Phys. (to appear).Google Scholar
  14. 14.
    W. Ochs, Rep. Math. Phys. 9, 331 (1976).CrossRefGoogle Scholar
  15. 15.
    A. Wehrl, Rev. Mod. Phys. 50, 221 (1978).CrossRefGoogle Scholar
  16. 16.
    W. Yourgrau and A. van der Merwe, in Cosmology, Fusion and other Matters ,E. Reines, editor (Colo. Univ. Press, Boulder, Colorado, 1972).Google Scholar

Copyright information

© Plenum Press, New York 1983

Authors and Affiliations

  • Jean-Paul Marchand
    • 1
  1. 1.Department of MathematicsUniversity of DenverDenverUSA

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