Lax-type equation unifying gradient systems in quantum and classical statistical models

  • Yoshio Uwano


In a previous paper, Y. Uwanoet al.: nlin/SI:0512004, the author made a short remark on a similarity between gradient systems on a quantum information space and on a classical one: One is on the space of regular relative-configurations of multi-qubit states of ordered tuples and the other is on the space of multinomial distributions studied by Y. Nakamura: Japan J. Indust. Appl. Math.10 (1993) 179. This paper aims to report very briefly a Lax-type equation unifying the gradient systems on the information spaces with quantum and with classical features.


02.30.Ik 03.67.-a 

Key words

Lax-type equation quantum search gradient systems information geometry 


  1. [1]
    L. Grover: inProceedings of the 28th Annual ACM Symposium on the Theory of Computing, 1996, p. 212; Amer. J. Phys.69 (2001) 769.Google Scholar
  2. [2]
    M.A. Nielsen and I.L. Chuang:Quantum Computation and Quantum Information, Cambridge University Press, Cambridge, 2000; and references therein.MATHGoogle Scholar
  3. [3]
    A. Miyake and M. Wadati: Phys. Rev. A64 (2001) 042317.Google Scholar
  4. [4]
    Y. Uwano, H. Hino, and Y. Ishiwatari: nlin/SI:0512004; Physics of Atomic Nuclei (2006), to appear.Google Scholar
  5. [5]
    Y. Uwano, H. Hino, and Y. Ishiwatari:Quantum information geometry around a quantum search for an ordered tuple of multi-qubit states, in preparation.Google Scholar
  6. [6]
    Y. Uwano, Y. Ishiwatari, and H. Hino:Integrable gradient system around a quantum search for an ordered tuple of multi-qubit states, in preparation.Google Scholar
  7. [7]
    Y. Nakamura: Jpn. J. Indust. Appl. Math.10 (1993) 179;11 (1994) 21.MATHCrossRefGoogle Scholar
  8. [8]
    A. Fujiwara and H. Nagaoka: Phys. Lett. A201 (1995) 119.MATHCrossRefADSMathSciNetGoogle Scholar

Copyright information

© Springer 2006

Authors and Affiliations

  • Yoshio Uwano
    • 1
  1. 1.Department of Complex SystemsSchool of Systems Information Science Future University HakodateHakodateJapan

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