Fundamental study on entropy and information in quantum information science

• Project/Area Number: 20740067
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Nihon University
• Principal Investigator: FURUICHI Shigeru (FURUICHI Sigeru) 日本大学, 文理学部, 准教授 (50299327)
• Project Period (FY): 2008 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000); Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2008: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
• 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 / skew information / 公理的特徴付 / 行列解析 / 情報理論 / エントロピー / 作用素論 / 情報科学 / Fisher情報量 / Wigner-Yasase skew information / Wigner-Yasase-Dyson skew information / 相対エントロピー / 一意性定理 / 情報幾何学 / Tsallisエントロピー / 関数解析 / 統計力学

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

• [Journal Article] Several applications of Cartwright-Field's inequality (2011)
  • 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 inequality (2011)
  • 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 equations (2011)
  • Author(s): S. Furuichi
  • Journal Title: Advances in Mathematical Physics Volume: Vol.2011 Issue: 1 Pages: 12-12
  • DOI: 10.1155/2011/126108
  • Peer Reviewed
• [Journal Article] Inequalities for Tsallis relative entropy and generalized skew information (2011)
  • Author(s): S. Furuichi
  • Journal Title: Linear and Multilinear algebra(Special issue on Quantum information science and Numerical ranges) Volume: Vol.59 Issue: 10 Pages: 1143-1158
  • DOI: 10.1080/03081087.2011.574624
  • Peer Reviewed
• [Journal Article] Refinements of the trace inequality of Belmega, Lasaulce and Debbah (2011)
  • 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 cup (2011)
  • 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 inequalities (2011)
  • 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] On refined Young inequalities and reverse inequalities (2011)
  • Author(s): S.Furuichi
  • Journal Title: Journal of Mathematical inequalities Volume: 5 Pages: 21-31
  • Peer Reviewed
• [Journal Article] Mathematical analyses of 2010 FIFA world cup (2011)
  • Author(s): S.Furuichi, H.Hino
  • Journal Title: Applied Mathematics and Information Science Volume: 5 Pages: 205-219
  • Peer Reviewed
• [Journal Article] Refinements of the trace inequality of Belmega, Lasaulce and Debbah (2011)
  • Author(s): S.Furuichi, M.Lin
  • Journal Title: Australian Journal of Mathematical Analysis and Applications Volume: 7 Pages: 1-4
  • Peer Reviewed
• [Journal Article] Characterizations of generalized entropy functions by functional equations (2011)
  • Author(s): S.Furuichi
  • Journal Title: Advances in Mathematical Physics Volume: 2011 Pages: 1-12
  • Peer Reviewed
• [Journal Article] Alternative reverse inequalities for Young's inequality (2011)
  • Author(s): S.Furuichi, N.Minculete
  • Journal Title: Journal of Mathematical inequalities Volume: 5 Pages: 595-600
  • Peer Reviewed
• [Journal Article] Several applications of Cartwright-Field's inequality (2011)
  • Author(s): N.Minculeten, S.Furuichi
  • Journal Title: International Journal of pure and applied mathematics Volume: 71 Pages: 19-30
  • Peer Reviewed
• [Journal Article] An axiomatic characterization of a two-parameter extended relative entropy (2010)
  • Author(s): S. Furuichi
  • Journal Title: Journal of Mathematical Physics Volume: Vol.51 Issue: 12
  • DOI: 10.1063/1.3525917
  • Peer Reviewed
• [Journal Article] Schrodinger uncertainty relation with Wigner-Yanase skew information (2010)
  • Author(s): S. Furuichi
  • Journal Title: Phys. Rev. A Volume: Vol.82 Issue: 3 Pages: 341010-341012
  • DOI: 10.1103/physreva.82.034101
  • Peer Reviewed
• [Journal Article] A matrix trace inequality and its application (2010)
  • Author(s): S. Furuichi and M. Lin
  • Journal Title: Linear Algebra and its Applications Volume: Vol.433 Issue: 7 Pages: 1324-1328
  • DOI: 10.1016/j.laa.2010.05.011
  • Peer Reviewed
• [Journal Article] An axiomatic characterization of a two-parameter extended relative entropy (2010)
  • Author(s): S.Furuichi
  • Journal Title: Journal of Mathematical Physics Vol.51
• [Journal Article] Schrodinger uncertainty relation with Wigner- Yanase skew information (2010)
  • Author(s): S.Furuichi
  • Journal Title: Phys.Rev.A Vol.82
• [Journal Article] A matrix trace inequality and its application (2010)
  • Author(s): S.Furuichi, M.Lin
  • Journal Title: Linear Algebra and its Applications Vol.433 Pages: 1324-1328
• [Journal Article] On generalized Fisher informations and Cremer-Rao type inequalities (2010)
  • Author(s): S.Furuichi
  • Journal Title: Journal of Physics : Conference Series Vol.201 Pages: 12016-12016
• [Journal Article] An axiomatic characterization of a two-parameter extended relative entropy (2010)
  • Author(s): S.Furuichi
  • Journal Title: Journal of Mathematical Physics Volume: 51
  • Peer Reviewed
• [Journal Article] Schrodinger uncertainty relation with Wigner-Yanase skew information (2010)
  • Author(s): S.Furuichi
  • Journal Title: Physical Review A Volume: 82
  • Peer Reviewed
• [Journal Article] A matrix trace inequality and its application (2010)
  • Author(s): S.Furuichi, M.Lin
  • Journal Title: Linear Algebra and its Applications Volume: 433 Pages: 1324-1328
  • Peer Reviewed
• [Journal Article] On generalized Fisher informations and Cremer-Rao type inequalities (2010)
  • Author(s): S.Furuichi
  • Journal Title: Journal of Physics : Conference Series Volume: 201
  • Peer Reviewed
• [Journal Article] Trace inequalities on a generalized Wigner-Yanase skew information (2009)
  • Author(s): S. Furuichi, K. Yanagi and K. Kuriyama
  • Journal Title: Journal of Mathematical Analysis and Applications Volume: Vol.356 Issue: 1 Pages: 179-185
  • DOI: 10.1016/j.jmaa.2009.02.043
  • Peer Reviewed
• [Journal Article] Note on matrix trace inequalities (2009)
  • Author(s): S. Furuichi, K. Kuriyama and K. Yanagi
  • Journal Title: Linear Algebra and its Applications Volume: Vol.430 Issue: 8-9 Pages: 2271-2276
  • 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 statistics (2009)
  • Author(s): S. Furuichi
  • Journal Title: Journal of Mathematical Physics Volume: Vol.50 Issue: 1
  • DOI: 10.1063/1.3063640
  • Peer Reviewed
• [Journal Article] On the maximum entropy principle and the minimization of the Fisher information in Tsallis statistics (2009)
  • Author(s): S. Furuichi
  • Journal Title: Journal of Mathematical Physics Vol.50
  • Peer Reviewed
• [Journal Article] Matrix trace inequalities on Tsallis entropies (2008)
  • Author(s): S. Furuichi
  • Journal Title: Journal of inequalities in pure and applied mathematics Volume: Vol.9 Pages: 7-7
  • URL: http://www.emis.de/journals/JIPAM/article935.html?sid=935
  • Peer Reviewed
• [Journal Article] Some operator inequalities and trace inequalities related to Tsallis entropy (2008)
  • Author(s): K. Yanagi, S. Furuichi and K. Kuriyama
  • Journal Title: Banach and function spaces II (Yokohama Publ.) Pages: 445-454
• [Journal Article] Generalized Wigner-Yanase skew information and generalized Fisher information (2008)
  • Author(s): K. Yanagi, S. Furuichi and K. Kuriyama
  • Journal Title: Proceedings of International Symposium on Information Theory and its Applications Pages: 455-460
• [Presentation] Belmega-Lasaulce-Debbahの行列トレース不等式の改良について (2012)
  • Author(s): 古市茂, M.Lin
  • Organizer: 日本数学会2012年度年会
  • Place of Presentation: 東京理科大学
  • Year and Date: 2012-03-27
• [Presentation] Skew informationに関するシュレーディンガー型の不確定性関係 (2011)
  • Author(s): 古市茂, 柳研二郎
  • Organizer: 第34回情報理論とその応用シンポジウム(SITA2011)
  • Place of Presentation: 岩手・森の風ホテル鶯宿
  • Year and Date: 2011-12-01
• [Presentation] 情報量とエントロピーに関連した不等式について (2011)
  • Author(s): 古市茂
  • Organizer: 作用素論・作用素環論研究集会
  • Place of Presentation: 琉球大学,研究者交流施設・50周年記念館
  • Year and Date: 2011-11-04
• [Presentation] Tsallis相対エントロピーの下界と上界について (2011)
  • Author(s): 古市茂
  • Organizer: ワークショップ:非加法的統計と情報幾何
  • Place of Presentation: 理化学研究所脳科学研究センター
  • Year and Date: 2011-10-12
• [Presentation] Metric adjusted skew informationとmetric adjusted correlation measureに関連する不確定性関係について (2011)
  • Author(s): 柳研二郎, 古市茂
  • Organizer: 日本数学会2011年度秋季総合分科会関数解析学分科会
  • Place of Presentation: 信州大学
  • Year and Date: 2011-09-30
• [Presentation] A matrix trace inequality and its applications to entropy theory (2011)
  • Author(s): S. Furuichi
  • Organizer: The 17th International Linear Algebra Society Conference, Technische Universitat Braunschweig
  • Place of Presentation: Braunschweig, Germany
• [Presentation] Refinements of Young inequality and two reverse inequalities for refined Young inequality (2011)
  • Author(s): S. Furuichi
  • Organizer: The 22nd International Workshop on Operator Theory and its Applications(IWOTA 2011)
  • Place of Presentation: Universidad de Sevilla
• [Presentation] Skew information, uncertainty relation and trace inequality (2011)
  • Author(s): S. Furuichi
  • Organizer: International conference QBIC 2011
  • Place of Presentation: Tokyo University of Science, Canal Hall Noda Campus, Chiba, Japan
• [Presentation] Refinements of Young inequality and two reverse inequalities for refined Young inequality (2011)
  • Author(s): S.Furuichi
  • Organizer: The 22nd International Workshop on Operator Theory and its Applications (IWOTA 2011)
  • Place of Presentation: Universidad de Sevilla
• [Presentation] A matrix trace inequality and its applications to entropy theory (2011)
  • Author(s): S.Furuichi
  • Organizer: The 17th International Linear Algebra Society Conference
  • Place of Presentation: Technische Universitat Braunschweig, Braunschweig, Germany
• [Presentation] Metric adjusted skew information and metric adjusted correlation measure (2011)
  • Author(s): K.Yanagi, S.Furuichi
  • Organizer: International Conference on Nonlinear Mathematics for Uncertainty and Its Applications (NLMUA2011)
  • Place of Presentation: Beijing University of Technology (BJUT), China
• [Presentation] ある行列トレース不等式とその一般化エントロピーへの応用 (2011)
  • Author(s): 古市茂
  • Organizer: 環瀬戸内応用数理研究部会第14回シンポジウム
  • Place of Presentation: 岡山理科大学
• [Presentation] 2010 FIFA World Cupの数学的解析 (2011)
  • Author(s): 古市茂, 日野英逸
  • Organizer: 環瀬戸内応用数理研究部会第14回シンポジウム
  • Place of Presentation: 岡山理科大学
• [Presentation] Skew information, uncertainty relation and trace inequality (2011)
  • Author(s): S.Furuichi
  • Organizer: International conference QBIC 2011
  • Place of Presentation: Chiba, Japan
• [Presentation] Youngの不等式の改良について (2010)
  • Author(s): 古市茂
  • Organizer: 日本数学会2010年度秋季総合分科会関数解析学分科会
  • Place of Presentation: 名古屋大学
  • Year and Date: 2010-09-23
• [Presentation] ある行列トレース不等式とその応用 (2010)
  • Author(s): 古市茂
  • Organizer: 日本数学会2010年度秋季総合分科会関数解析学分科会
  • Place of Presentation: 名古屋大学
  • Year and Date: 2010-09-23
• [Presentation] On trace inequalities related to skew informations and generalized relative entropies (2010)
  • Author(s): S. Furuichi
  • Organizer: Information Geometry and its Applications III
  • Place of Presentation: Leipzig, Germany
• [Presentation] A refined Young inequality and related results (2010)
  • Author(s): S. Furuichi
  • Organizer: The 16th International Linear Algebra Society Conference
  • Place of Presentation: Pisa, Italy
• [Presentation] トレース不等式とその応用 (2010)
  • Author(s): 古市茂
  • Organizer: 研究集会「独立性と従属性の数理-関数解析学の視点から-」
  • Place of Presentation: 京都大学数理解析研究所
• [Presentation] 一般化エントロピー関数の特徴付けと一意性定理について (2010)
  • Author(s): 古市茂
  • Organizer: 第33回情報理論とその応用シンポジウム(SITA2010)
  • Place of Presentation: 長野・信州松代ロイヤルホテル
• [Presentation] On trace inequalities related to skew informations and generalized relative entropies (2010)
  • Author(s): S.Furuichi
  • Organizer: Information Geometry and its Applications III
  • Place of Presentation: Leipzig, Germany(invited lecture)
• [Presentation] On trace inequalities related to skew informations and generalized relative entropies (2010)
  • Author(s): S.Furuichi
  • Organizer: Information Geometry and its Applications III
  • Place of Presentation: Leipzig, Germany(招待講演)
• [Presentation] 一般化エントロピテ関数の特徴付けと一意性定理について (2010)
  • Author(s): 古市茂
  • Organizer: 第33回情報理論とその応用シンポジウム(SITA2010)
  • Place of Presentation: 長野・信州松代ロイヤルホテル
• [Presentation] ペロン-フロベニウスの定理と重み付き関数に基づいたランキング法-2010FIFA World Cupを例に- (2010)
  • Author(s): 古市茂, 日野英逸
  • Organizer: 研究集会「独立性と従属性の数理-関数解析学の視点から-」
  • Place of Presentation: 京都大学数理解析研究所
• [Presentation] A variational expression for generalized relative entropy (2009)
  • Author(s): S. Furuichi
  • Organizer: The Second Najman Conference on Spectral Problems for Operators and Matrices
  • Place of Presentation: Dubrovnik, Croatia
• [Presentation] Generalized Wigner-Yanase Skew Information and Generalized Fisher Information (2008)
  • Author(s): K. Yanagi, S. Furuichi and K. Kuriyama
  • Organizer: ISITA2008
  • Place of Presentation: Auckland, New Zealand
  • Year and Date: 2008-12-08
• [Presentation] 量子情報理論における不等式について (2008)
  • Author(s): 古市茂, 柳研二郎
  • Organizer: 環瀬戸内応用数理研究部会
  • Place of Presentation: 山形大学
  • Year and Date: 2008-10-10
• [Presentation] Wigner-Yanasc-Dyson skew informationに関する不等式, III (2008)
  • Author(s): 古市茂, 柳研二郎, 栗山憲
  • Organizer: 日本数学会2008年度秋季総合分科会函数解析学分科会
  • Place of Presentation: 東京工業大学
  • Year and Date: 2008-09-24
• [Presentation] Matrix trace inequalities on a generalized Wigner-Yanase skew information (2008)
  • Author(s): S. Furuichi
  • Organizer: International Workshop on Operator Theory and Its Applications(IWOTA2008)
  • Place of Presentation: Virginia, USA
  • Year and Date: 2008-07-22
• [Presentation] 一般化されたskew infbrmationに関連した不確定性関係 (2008)
  • Author(s): 柳研二郎, 古市茂, 栗山憲
  • Organizer: 研究集会「バナッハ空間及び関数空間論の最近の進展とその応用」
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2008-06-05
• [Presentation] On trace inequalities for products of matrices (2008)
  • Author(s): S. Furuichi, K. Kuriyama and K. Yanagi
  • Organizer: 15th International Linear Algebra Society Conference
  • Place of Presentation: Cancun, Mexico
• [Presentation] Matrix trace inequalities on a generalized Wigner-Yanase skew information (2008)
  • Author(s): S. Furuichi
  • Organizer: International Workshop on Operator Theory and Its Applications(IWOTA2008)
  • Place of Presentation: College of William and Mary, Virginia, USA