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2011 Fiscal Year Final Research Report

Fundamental study on entropy and information in quantum information science

Research Project

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Project/Area Number 20740067
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionNihon University

Principal Investigator

FURUICHI Shigeru  日本大学, 文理学部, 准教授 (50299327)

Project Period (FY) 2008 – 2011
Keywords量子情報理論 / 量子エントロピー / 一般化エントロピー / Skew information / トレース不等式 / 情報幾何 / 不確定性関係
Research Abstract

I studied the mathematical and fundamental studies for entropies and informations in quantum information theory, and then obtained several important results. For example, I established the Schrodinger type uncertainty relation by using Wigner-Yanase skew information and a lower bound for the Tsallis relative entropy by applying the matrix trace inequality.

  • Research Products

    (22 results)

All 2011 2010 2009 2008

All Journal Article (14 results) (of which Peer Reviewed: 14 results) Presentation (8 results)

  • [Journal Article] Several applications of Cartwright-Field's inequality2011

    • Author(s)
      N. Minculeten and S. Furuichi
    • Journal Title

      International Journal of pure and applied mathematics

      Volume: Vol.71, No.1 Pages: 19-30

    • URL

      http://ijpam.eu/contents/2011-71-1/2/index.html

    • Peer Reviewed
  • [Journal Article] Alternative reverse inequalities for Young's inequality2011

    • Author(s)
      S. Furuichi, and N. Minculete
    • Journal Title

      Journal of Mathematical inequalities

      Volume: Vol.5 Pages: 595-600

    • URL

      http://files.ele-math.com/articles/jmi-05-51.pdf

    • Peer Reviewed
  • [Journal Article] Characterizations of generalized entropy functions by functional equations2011

    • Author(s)
      S. Furuichi
    • Journal Title

      Advances in Mathematical Physics

      Volume: Vol.2011 Pages: 12

    • DOI

      DOI:10.1155/2011/126108

    • Peer Reviewed
  • [Journal Article] Inequalities for Tsallis relative entropy and generalized skew information2011

    • Author(s)
      S. Furuichi
    • Journal Title

      Linear and Multilinear algebra(Special issue on Quantum information science and Numerical ranges)

      Volume: Vol.59 Pages: 1143-1158

    • DOI

      DOI:10.1080/03081087.2011.574624

    • Peer Reviewed
  • [Journal Article] Refinements of the trace inequality of Belmega, Lasaulce and Debbah2011

    • Author(s)
      S. Furuichi and M. Lin
    • Journal Title

      Australian Journal of Mathematical Analysis and Applications

      Volume: Vol.7 Pages: 1-4

    • URL

      http://ajmaa.org/cgi-bin/paper.pl?string=v7n2/V7I2P23.tex

    • Peer Reviewed
  • [Journal Article] Mathematical analyses of 2010 FIFA world cup2011

    • Author(s)
      S. Furuichi and H. Hino
    • Journal Title

      Applied Mathematics and Information Science

      Volume: Vol.5, No.2 Pages: 205-219

    • URL

      http://naturalspublishing.com/Article.asp?ArtcID=107

    • Peer Reviewed
  • [Journal Article] On refined Young inequalities and reverse inequalities2011

    • Author(s)
      S. Furuichi
    • Journal Title

      Journal of Mathematical inequalities

      Volume: Vol.5 Pages: 21-31

    • URL

      http://files.ele-math.com/articles/jmi-05-03.pdf

    • Peer Reviewed
  • [Journal Article] An axiomatic characterization of a two-parameter extended relative entropy2010

    • Author(s)
      S. Furuichi
    • Journal Title

      Journal of Mathematical Physics

      Volume: Vol.51 Pages: 123302-1-123302-10

    • DOI

      DOI:10.1063/1.3525917

    • Peer Reviewed
  • [Journal Article] Schrodinger uncertainty relation with Wigner-Yanase skew information2010

    • Author(s)
      S. Furuichi
    • Journal Title

      Phys. Rev. A

      Volume: Vol.82 Pages: 0341010-0341012

    • DOI

      DOI:10.1103/PhysRevA.82.034101

    • Peer Reviewed
  • [Journal Article] A matrix trace inequality and its application2010

    • Author(s)
      S. Furuichi and M. Lin
    • Journal Title

      Linear Algebra and its Applications

      Volume: Vol.433 Pages: 1324-1328

    • DOI

      DOI:10.1016/j.laa.2010.05.011

    • Peer Reviewed
  • [Journal Article] Trace inequalities on a generalized Wigner-Yanase skew information2009

    • Author(s)
      S. Furuichi, K. Yanagi and K. Kuriyama
    • Journal Title

      Journal of Mathematical Analysis and Applications

      Volume: Vol.356 Pages: 179-185

    • DOI

      DOI:10.1016/j.jmaa.2009.02.043

    • Peer Reviewed
  • [Journal Article] Note on matrix trace inequalities2009

    • Author(s)
      S. Furuichi, K. Kuriyama and K. Yanagi
    • Journal Title

      Linear Algebra and its Applications

      Volume: Vol.430 Pages: 2271-2276

    • DOI

      DOI:10.1016/j.laa.2008.12.003

    • Peer Reviewed
  • [Journal Article] On the maximum entropy principle and the minimization of the Fisher information in Tsallis statistics2009

    • Author(s)
      S. Furuichi
    • Journal Title

      Journal of Mathematical Physics

      Volume: Vol.50 Pages: 013303-1-013303-12

    • DOI

      DOI:10.1063/1.3063640

    • Peer Reviewed
  • [Journal Article] Matrix trace inequalities on Tsallis entropies2008

    • Author(s)
      S. Furuichi
    • Journal Title

      Journal of inequalities in pure and applied mathematics

      Volume: Vol.9 Pages: 7

    • URL

      http://www.emis.de/journals/JIPAM/article935.html?sid=935

    • Peer Reviewed
  • [Presentation] A matrix trace inequality and its applications to entropy theory2011

    • Author(s)
      S. Furuichi
    • Organizer
      The 17th International Linear Algebra Society Conference, Technische Universitat Braunschweig
    • Place of Presentation
      Braunschweig, Germany
    • Year and Date
      20110822-26
  • [Presentation] Refinements of Young inequality and two reverse inequalities for refined Young inequality2011

    • Author(s)
      S. Furuichi
    • Organizer
      The 22nd International Workshop on Operator Theory and its Applications(IWOTA 2011)
    • Place of Presentation
      Universidad de Sevilla
    • Year and Date
      20110703-09
  • [Presentation] Skew information, uncertainty relation and trace inequality2011

    • Author(s)
      S. Furuichi
    • Organizer
      International conference QBIC 2011
    • Place of Presentation
      Tokyo University of Science, Canal Hall Noda Campus, Chiba, Japan
    • Year and Date
      20110307-14
  • [Presentation] On trace inequalities related to skew informations and generalized relative entropies2010

    • Author(s)
      S. Furuichi
    • Organizer
      Information Geometry and its Applications III
    • Place of Presentation
      Leipzig, Germany
    • Year and Date
      20100802-06
  • [Presentation] A refined Young inequality and related results2010

    • Author(s)
      S. Furuichi
    • Organizer
      The 16th International Linear Algebra Society Conference
    • Place of Presentation
      Pisa, Italy
    • Year and Date
      20100621-25
  • [Presentation] A variational expression for generalized relative entropy2009

    • Author(s)
      S. Furuichi
    • Organizer
      The Second Najman Conference on Spectral Problems for Operators and Matrices
    • Place of Presentation
      Dubrovnik, Croatia
    • Year and Date
      20090511-16
  • [Presentation] Matrix trace inequalities on a generalized Wigner-Yanase skew information2008

    • Author(s)
      S. Furuichi
    • Organizer
      International Workshop on Operator Theory and Its Applications(IWOTA2008)
    • Place of Presentation
      College of William and Mary, Virginia, USA
    • Year and Date
      20080722-26
  • [Presentation] On trace inequalities for products of matrices2008

    • Author(s)
      S. Furuichi, K. Kuriyama and K. Yanagi
    • Organizer
      15th International Linear Algebra Society Conference
    • Place of Presentation
      Cancun, Mexico
    • Year and Date
      20080616-20

URL: 

Published: 2013-07-31  

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