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2005 Fiscal Year Final Research Report Summary

Information Geometry for Quantum Systems and Its Applications

Research Project

Project/Area Number 15500004
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Fundamental theory of informatics
Research InstitutionThe University of Electro-Communications

Principal Investigator

NAGAOKA Hiroshi  UEC, Grad.School of Information Systems., Assoc.Prof., 大学院・情報システム学研究科, 助教授 (80192235)

Co-Investigator(Kenkyū-buntansha) HAN Te Sun  UEC, Grad.School of Information Systems., Professor, 大学院・情報システム学研究科, 教授 (80097287)
FUJIWARA Akio  Osaka University, Grad.School of Science, Professor, 大学院・理学研究科, 教授 (30251359)
Project Period (FY) 2003 – 2005
Keywordsinformation geometry / quantum information geometry / quantum information theory / quantum estimation / relative entropy
Research Abstract

This research project aims at deepening information geometry for quantum systems from a statistical/information-theoretical viewpoint and also at investigating new aspects of statistical/information-theoretical problems for quantum systems from a geometrical viewpoint, mainly focusing upon quantum estimation theory and quantum relative entropy. Main results are as follows.
1.We have provided various quantum analogues of the Fisher metric and the (alpha=1,-1)-connections on the space of faithful quantum states with a unifying theoretical framework and have studied the general theory of quantum information-geometrical structure as well as physical/information-theoretical significance of some specific structures.
2.We have demonstrated several information-geometrical aspects of a manifold of quantum pure states, among which are a close relation between the dually flat structure and the Kaehler structure for a quantum exponential family of pure states and an extension of the RLD metric on the complexified cotangent space.
3.The Boltzmann machine is a kind of stochastic neural network and is known to be fit to the framework of information geometry by the fact that its equilibrium distributions form an exponential family. We have studied a quantum extension of Boltzmann machine from an information-geometrical viewpoint to clarify analogy and difference between the classical and quantum cases.
4.We have also investigated several related subjects on estimation theory for quantum channels, classical and quantum information theory and information geometry for stochastic processes.

  • Research Products

    (12 results)

All 2005 2004 2003

All Journal Article (11 results) Book (1 results)

  • [Journal Article] A quantum/complex extension of information geometry2005

    • Author(s)
      H.Nagaoka
    • Journal Title

      Proc. 2nd International Symposium on Information Geometry and Its Applications

      Pages: 177-180

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] A quantum extension of Boltzmann machine : an information geometrical approach2005

    • Author(s)
      N.Yapage, H.Nagaoka
    • Journal Title

      Proc.Erato conference on Quantum Information Science (EQIS)

      Pages: 204-205

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] An extension of asymptotically sufficient statistic method for pointwise strong universality2005

    • Author(s)
      M.Arimura, H.Nagaoka
    • Journal Title

      Proc.2005 IEEE International Symposium on Information Theory (ISIT2005)

      Pages: 505-509

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] A quantum/complex extension of information geometry2005

    • Author(s)
      H.Nagaoka
    • Journal Title

      Proc.2nd International Symposium on Information Geometry and Its Applications

      Pages: 177-480

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] A quantum extension of Boltzmann machine : an information geometrical approach2005

    • Author(s)
      N.Yapage, H.Nagaoka
    • Journal Title

      Proc.Erato conference on Quantu Information Science (EQIS)

      Pages: 204-205

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] An extension of asymptotically sufficient statistic method for pointwise strong universality2005

    • Author(s)
      M.Arimua, H.Nagaoka
    • Journal Title

      Proc.2005 IEEE International Symposium on Information Tehory (ISIT2005)

      Pages: 505-509

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] The world of quantum information geometry (in Japanese)2005

    • Author(s)
      H.Nagaoka
    • Journal Title

      IEICE Trans.A J88-A・8

      Pages: 874-885

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Asymptotic Theory of Quantum Statistical Inference : Selected Papers2005

    • Author(s)
      M.Hayashi (ed.)
    • Journal Title

      World Scientific

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Statistical estimation of a quantum operation2004

    • Author(s)
      A.Fujiwara
    • Journal Title

      Quantum Information, Statistics, Probability(ed.O.Hirota)

      Pages: 78-89

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Statistical estimation of a quantum operation2004

    • Author(s)
      A.Fujiwara
    • Journal Title

      Quantum Information, Statistics, Probaility, ed.O.Hirota

      Pages: 78-89

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] General formulas for capacity of classical-quantum channels2003

    • Author(s)
      M.Hayashi, H.Nagaoka
    • Journal Title

      IEEE Trans.Inform.Theory 49・7

      Pages: 1753-1768

    • Description
      「研究成果報告書概要(和文)」より
  • [Book] Asymptotic Theory of Quantum Statistical Inference : Selected Papers2005

    • Author(s)
      M.Hayashi(ed.)
    • Total Pages
      542
    • Publisher
      World Scientific
    • Description
      「研究成果報告書概要(和文)」より

URL: 

Published: 2007-12-13  

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