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Mathematical studies on quantum entropy and its applications to information science

Research Project

Project/Area Number 24540146
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionNihon University

Principal Investigator

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

Project Period (FY) 2012-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywords量子エントロピー / ダイヴァージェンス / 作用素不等式 / ハイポエントロピー / エントロピー / 行列解析 / 不等式 / 情報量 / 作用素平均 / 正作用素(正定値行列) / Skew information / 不確定性関係 / 平均 / 一般化エントロピー
Outline of Final Research Achievements

I have published 9 peer-reviewed papers and gave my presentations through this research plroject. The main results are as follows.
I obtained the upper and lower bounds for the generalized entropy and gave the estimation of the upper and lower bounds for Tsallis relative operator entropy. In addition, I derived the Schrodinger type uncertainty relation by metric adjusted skew correlation. Moreover, I studied the mathematical properties for
hypoentropy and hypodivergence. I also gave the further results for the generalized hypoentropy and hypodivergence.

Report

(5 results)
  • 2015 Annual Research Report   Final Research Report ( PDF )
  • 2014 Research-status Report
  • 2013 Research-status Report
  • 2012 Research-status Report
  • Research Products

    (31 results)

All 2016 2015 2014 2013 2012

All Journal Article (13 results) (of which Peer Reviewed: 12 results,  Acknowledgement Compliant: 5 results,  Open Access: 5 results) Presentation (18 results) (of which Int'l Joint Research: 3 results,  Invited: 1 results)

  • [Journal Article] Estimations of Heron means for positive operators2016

    • Author(s)
      Masatoshi Fujii, Shigeru Furuichi, Ritsuo Nakamoto
    • Journal Title

      Journal of Mathematical Inequalities

      Volume: 10 Issue: 1 Pages: 19-30

    • DOI

      10.7153/jmi-10-02

    • Related Report
      2015 Annual Research Report
    • Open Access
  • [Journal Article] Precise estimates of bounds on relative operator entropies2015

    • Author(s)
      Shigeru Furuichi
    • Journal Title

      Mathematical Inequalities & Applications

      Volume: 18 Issue: 3 Pages: 1331-4343

    • DOI

      10.7153/mia-18-63

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Operator inequalities associated with relative operator entropies2015

    • Author(s)
      Mohammad Bagher Ghaemi, Nahid Gharakhanlu, and Shigeru Furuichi
    • Journal Title

      Advances in Inequalities and Applications

      Volume: 2015 Pages: 1-21

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Unitarily invariant norm inequalities for some means2014

    • Author(s)
      Shigeru Furuichi
    • Journal Title

      Journal of Inequalities and Applications

      Volume: 2014 Issue: 1 Pages: 1-11

    • DOI

      10.1186/1029-242x-2014-158

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Operator inequalities among arithmetic mean, geometric mean and harmonic mean2014

    • Author(s)
      Shigeru Furuichi
    • Journal Title

      Journal of Mathematical Inequalities

      Volume: 8 Issue: 3 Pages: 669-672

    • DOI

      10.7153/jmi-08-49

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] On Some Properties of Tsallis Hypoentropies and Hypodivergences2014

    • Author(s)
      Shigeru Furuichi, Flavia-Corina Mitroi-Symeonidis and Eleutherius Symeonidis
    • Journal Title

      Entropy

      Volume: 16 Issue: 10 Pages: 5377-5399

    • DOI

      10.3390/e16105377

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] GENERALIZED DIFFERENCES AND ABEL'S TYPE BINOMIAL THEOREMS2014

    • Author(s)
      Ken Kuriyama, and Shigeru Furuichi
    • Journal Title

      International Journal of Pure and Applied Mathematics

      Volume: 96 Issue: 2 Pages: 189-196

    • DOI

      10.12732/ijpam.v96i2.3

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Bounds of the logarithmic mean2013

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

      Journal of Inequalities and Applications

      Volume: 535 Issue: 1 Pages: 1-11

    • DOI

      10.1186/1029-242x-2013-535

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Uncertainty relations for generalized metric adjusted skew information and generalized metric adjusted correlation measure2013

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

      Journal of Uncertainty Analysis and Applications

      Volume: 1 Issue: 1 Pages: 1-14

    • DOI

      10.1186/2195-5468-1-12

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Refined Young Inequalities with Specht's Ratio2012

    • Author(s)
      Shigeru Furuichi
    • Journal Title

      Journal of the Egyptian Mathematical Society

      Volume: 20 Issue: 1 Pages: 46-49

    • DOI

      10.1016/j.joems.2011.12.010

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Some inequalities on generalized entropies2012

    • Author(s)
      Shigeru Furuichi, Nicusor Minculete and Flavia C. Mitroi
    • Journal Title

      Journal of Inequalities and Applications

      Volume: 226 Issue: 1 Pages: 1-17

    • DOI

      10.1186/1029-242x-2012-226

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Schrödinger uncertainty relation, Wigner–Yanase–Dyson skew information and metric adjusted correlation measure2012

    • Author(s)
      Kenjiro Yanagi and Shigeru Furuichi
    • Journal Title

      Journal of Mathematical Analysis and Applications

      Volume: 388 Issue: 2 Pages: 1147-1156

    • DOI

      10.1016/j.jmaa.2011.10.061

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Mathematical inequalities for some divergences2012

    • Author(s)
      Shigeru Furuichi and Nicusor Minculete
    • Journal Title

      Physica A

      Volume: 391 Issue: 1-2 Pages: 388-400

    • DOI

      10.1016/j.physa.2011.07.052

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Presentation] On some mathematical inequalities for some entropies2015

    • Author(s)
      Shigeru Furuichi
    • Organizer
      The Seventh International Conference on Information
    • Place of Presentation
      National Taiwan University, Taipei, Taiwan
    • Year and Date
      2015-11-25
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 正作用素に対するHeron mean に関連した不等式2015

    • Author(s)
      Masatoshi Fujii, Shigeru Furuichi, Ritsuo Nakamoto
    • Organizer
      日本数学会・2015年度秋季総合分科会
    • Place of Presentation
      京都産業大
    • Year and Date
      2015-09-13
    • Related Report
      2015 Annual Research Report
  • [Presentation] On some properties of Tsallis hypoentropies and hypodivergences2015

    • Author(s)
      Flavia-Corina Mitroi-Symeonidis, Eleutherius Symeonidis and Shigeru Furuichi
    • Organizer
      The eighth congress of Romanian Mathematicians
    • Place of Presentation
      University "Al.I. Cuza", Iasi, Romania
    • Year and Date
      2015-06-26
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Some inequalities related to operator means2015

    • Author(s)
      Shigeru Furuichi
    • Organizer
      The eighth congress of Romanian Mathematicians
    • Place of Presentation
      University "Al.I. Cuza", Iasi, Romania
    • Year and Date
      2015-06-26
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] ある平均に関するユニタリ不変ノルム不等式と作用素不等式について2014

    • Author(s)
      古市茂
    • Organizer
      日本応用数理学会環瀬戸内応用数理研究部会第18回シンポジウム
    • Place of Presentation
      岡山県倉敷市
    • Year and Date
      2014-12-05 – 2014-12-07
    • Related Report
      2014 Research-status Report
  • [Presentation] 相対作用素エントロピーの上界と下界について2014

    • Author(s)
      古市茂
    • Organizer
      日本数学会2014年度秋季総合分科会 函数解析分科会
    • Place of Presentation
      広島大学
    • Year and Date
      2014-09-25 – 2014-09-28
    • Related Report
      2014 Research-status Report
  • [Presentation] On some unitarily invariant norm inequalities2014

    • Author(s)
      Shigeru Furuichi
    • Organizer
      IWOTA 2014
    • Place of Presentation
      Amsterdam, The Netherland
    • Year and Date
      2014-07-15 – 2014-07-20
    • Related Report
      2014 Research-status Report
  • [Presentation] Operator inequalities for some means and entropies2014

    • Author(s)
      Shigeru Furuichi
    • Organizer
      Mathematical inequalities and applications 2014
    • Place of Presentation
      Trogir, Croatia
    • Year and Date
      2014-06-21 – 2014-06-28
    • Related Report
      2014 Research-status Report
  • [Presentation] 対数平均の上界と下界について2014

    • Author(s)
      S.Furuichi and K.Yanagi
    • Organizer
      日本応用数理学会環瀬戸内応用数理研究部会第 17 回シンポジウム
    • Place of Presentation
      愛媛大学
    • Related Report
      2013 Research-status Report
  • [Presentation] ある平均に関するユニタリ不変ノルム不等式2014

    • Author(s)
      S.Furuichi
    • Organizer
      日本数学会2014年度年会 函数解析学分科会
    • Place of Presentation
      学習院大学
    • Related Report
      2013 Research-status Report
  • [Presentation] Mathematical inequalities on generalized entropies and divergences2013

    • Author(s)
      S. Furuichi, N. Minculete and F.-C. Mitroi
    • Organizer
      The Sixth International Conference on Information
    • Place of Presentation
      東京
    • Related Report
      2013 Research-status Report
  • [Presentation] Matrix inequalities on some means2013

    • Author(s)
      S.Furuichi
    • Organizer
      von Neumann seminar in Renyi institute
    • Place of Presentation
      Budapest
    • Related Report
      2013 Research-status Report
  • [Presentation] Generalizations of uncertainty relations with skew information2013

    • Author(s)
      K.Yanagi, S.Furuichi and K.Kuriyama
    • Organizer
      The Eighth International Conference on Nonlinear Analysis and Convex Analysis
    • Place of Presentation
      Hirosaki University
    • Related Report
      2013 Research-status Report
  • [Presentation] 一般化歪情報量に関する不確定性関係2013

    • Author(s)
      K.Yanagi, S.Furuichi and K.Kuriyama
    • Organizer
      日本数学会2013年度秋季総合分科会
    • Place of Presentation
      愛媛大学
    • Related Report
      2013 Research-status Report
  • [Presentation] Concavity of an auxiliary mean function and its application2013

    • Author(s)
      K.Yanagi, S.Furuichi and K.Kuriyama
    • Organizer
      実解析学シンポジウム2013
    • Place of Presentation
      岡山大学
    • Related Report
      2013 Research-status Report
  • [Presentation] ある補助平均函数の凹性と一般化歪情報量の不確定性関係2013

    • Author(s)
      K.Yanagi, S.Furuichi and K.Kuriyama
    • Organizer
      第36回情報理論とその応用学会シンポジウム
    • Place of Presentation
      伊東市
    • Related Report
      2013 Research-status Report
  • [Presentation] On some trace inequalities2012

    • Author(s)
      Shigeru Furuichi
    • Organizer
      One hour invited lecture for the seminar in Academy of Mathematics and Systems Sicence, Chinese Academy of Sicence.
    • Place of Presentation
      Chinese Academy of Sicence
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] On some refinements of Young inequalities for positive operators2012

    • Author(s)
      Shigeru Furuichi
    • Organizer
      The Seventh International Workshop on Matrices and Operators
    • Place of Presentation
      Harbin
    • Related Report
      2012 Research-status Report

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Published: 2013-05-31   Modified: 2019-07-29  

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