Research on Inequalities related to several kinds of entropies in classical or quantum system

• Project/Area Number: 26400119
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Josai University (2016-2017); Yamaguchi University (2014-2015)
• Principal Investigator: Yanagi Kenjiro 城西大学, 理学部, 客員教授 (90108267)
• Co-Investigator(Kenkyū-buntansha): 柳原 宏 山口大学, 大学院創成科学研究科, 教授 (30200538)
• Co-Investigator(Renkei-kenkyūsha): Furuichi Shigeru 日本大学, 文理学部, 教授 (50299327) ; Kuriyama Ken 佛教大学, 教育学部, 教授 (10116717)
• Project Period (FY): 2014-04-01 – 2018-03-31
• Project Status: Completed (Fiscal Year 2017)
• Budget Amount: ¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000); Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
• Keywords: 量子情報理論 / エントロピー / 不確定性関係 / トレース不等式 / 歪情報量 / 忠実度 / トレース距離 / 国際情報交流・台湾

Outline of Final Research Achievements

We obtained several non-hermitian uncertainty relations or sum types of uncertainty relations for generalized quasi-metric adjusted skew informations.

Research Products

• [Journal Article] On bounds for symmetric divergence measure (2017)
  • Author(s): Shigeru Furuichi, Kenjiro Yanagi, Ken Kuriyama
  • Journal Title: Journal of Physics, Conference Series Volume: 1853 Pages: 1-7
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] トレース不等式から見た不確定性関係 (2017)
  • Author(s): Kenjiro Yanagi
  • Journal Title: 京都大学数理解析研究所講究録 Volume: 2041 Pages: 175-183
• [Journal Article] On sum type uncertainty relations (2017)
  • Author(s): Kenjiro Yanagi
  • Journal Title: 実解析学シンポジウム報告集 Volume: 49 Pages: 53-58
• [Journal Article] 和型不確定性関係を表すトレース不等式について (2017)
  • Author(s): Kenjiro Yanagi
  • Journal Title: Proceedings of the 40th Symposium on Information Theory and its Applications Volume: 40 Pages: 335-340
• [Journal Article] Generalized Schrodinger uncertainty relation associated with a monotone or anti-monotone pair skew information (2017)
  • Author(s): Kenjiro Yanagi, Minato Tomonari
  • Journal Title: Journal of Nonlinear and Convex Analysis Volume: 18 Pages: 1547-1561
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Some generalizations of non-hermitian uncertainty relation described by the generalized quasi-metric adjusted skew information (2017)
  • Author(s): Kenjiro Yanagi
  • Journal Title: Linear and Nonlinear Analysis Volume: 3 Pages: 343-348
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] 忠実度とトレース距離に関する不等式の一般化について (2016)
  • Author(s): Kenjiro Yanagi
  • Journal Title: Proceedings of the 39th Symposium on Information Theory and its Applications Volume: 39 Pages: 495-499
  • Acknowledgement Compliant
• [Journal Article] Generalized trace inequalities related to fidelity and trace distance (2016)
  • Author(s): Kenjiro Yanagi
  • Journal Title: Linear and Nonlinear Analysis Volume: 2 Pages: 263-270
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Non-hermitian extension of uncertainty relation (2016)
  • Author(s): Kenjiro Yanagi
  • Journal Title: Journal of Nonlinear and Convex Analysis Volume: 17 Pages: 17-26
  • NAID: 120005516325
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] On the trace inequalities of left-right multiplication operators (2015)
  • Author(s): Kenjiro Yanagi
  • Journal Title: 2015実解析学シンポジウム報告集 Volume: 47 Pages: 57-62
  • Acknowledgement Compliant
• [Journal Article] Generalized trace inequalities related to fidelity and trace distance (2015)
  • Author(s): Kenjiro Yanagi
  • Journal Title: Proceedings of the Seventh International Conference on INFORMATION Volume: 7 Pages: 199-202
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Non-hermitian extensions of Heisenberg type and Schrodinger type uncertainty relations (2015)
  • Author(s): Kenjiro Yanagi, Kohei Sekikawa
  • Journal Title: Journal of Inequalities and Applications Volume: - Pages: 1-9
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Circular symmetrization, subordination and arclength problems on convex functions (2015)
  • Author(s): Mari Okada, S.Ponnusamy, A.Vasudevarao, Hiroshi Yanagihara
  • Journal Title: Math. Nach. Volume: -
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Non-hermitian extension of uncertainty relation (2014)
  • Author(s): Kenjiro Yanagi
  • Journal Title: 数理解析研究所講究録 Volume: 1906 Pages: 59-68
  • NAID: 120005516325
  • Open Access / Acknowledgement Compliant
• [Journal Article] Non-hermitian extensions of Schrodinger type uncertainty relations (2014)
  • Author(s): Kenjiro Yanagi
  • Journal Title: Proceedings of International Symposium on Information Theory and its Applications Volume: 2014 Pages: 163-166
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] 非エルミート型の不確定性関係とその応用 (2014)
  • Author(s): Kenjiro Yanagi
  • Journal Title: Proceedings of the 37th Symposium on Information Theory and its Applications Volume: 37 Pages: 674-678
  • NAID: 120006665773
  • Open Access / Acknowledgement Compliant
• [Journal Article] Radius of convexity of partial sums of functions in the vlose-to-convex family (2014)
  • Author(s): Saminathan Ponnusamy
  • Journal Title: Nonlinear Analysis Volume: 95 Pages: 219-228
  • DOI: 10.1016/j.na.2013.09.009
  • Peer Reviewed
• [Presentation] トレース不等式から見た不確定性関係Ⅱ (2018)
  • Author(s): 柳研二郎
  • Organizer: 京都大学数理解析研究所・研究集会「関数空間の深化とその周辺」
• [Presentation] 古典系および量子系におけるエントロピーなどの情報量の周辺について (2017)
  • Author(s): Kenjiro Yanagi
  • Organizer: 日本数学会実函数論分科会特別講演
  • Place of Presentation: 首都大学東京(八王子市)
  • Year and Date: 2017-03-24
  • Invited
• [Presentation] トレース不等式から見た不確定性関係 (2017)
  • Author(s): Kenjiro Yanagi
  • Organizer: 京都大学数理解析研究所・研究集会「関数空間の構造とその周辺」
  • Place of Presentation: 京都大学(京都市)
  • Year and Date: 2017-02-06
• [Presentation] トレース不等式から見た不確定性関係 (2017)
  • Author(s): 柳研二郎
  • Organizer: 京都大学数理解析研究所・研究集会「関数空間の構造とその周辺」
• [Presentation] 古典系および量子系におけるエントロピーなどの情報量の周辺について (2017)
  • Author(s): 柳研二郎
  • Organizer: 日本数学会
  • Invited
• [Presentation] Sum type uncertainty relations described by generalized quasi-metric adjusted skew informations (2017)
  • Author(s): Kenjiro Yanagi
  • Organizer: The 10th International Conference on Nonlinear Analysis amd Convex Analysis
  • Int'l Joint Research
• [Presentation] On trace inequalities for generalized quasi-metric adjusted skew informations (2017)
  • Author(s): Kenjiro Yanagi
  • Organizer: 6th International Eurasian Conference on Mathematical Sciences and Applications
  • Int'l Joint Research
• [Presentation] On sum type uncertainty relations (2017)
  • Author(s): 柳研二郎
  • Organizer: 実解析学シンポジウム
• [Presentation] 和型不確定性関係を表すトレース不等式について (2017)
  • Author(s): 柳研二郎
  • Organizer: 第40回情報理論とその応用シンポジウム
• [Presentation] 忠実度とトレース距離に関する不等式の一般化について (2016)
  • Author(s): Kenjiro Yanagi
  • Organizer: 第39回情報理論とその応用シンポジウム
  • Place of Presentation: 高山グリーンホテル(高山市)
  • Year and Date: 2016-12-13
• [Presentation] Some trace inequalities for left-right multiplication operators related to fidelity and trace distance (2016)
  • Author(s): Kenjiro Yanagi
  • Organizer: The 6th International Conference on Nonlinear Analysis and Optimization
  • Place of Presentation: Toki Messe(NIIgata)
  • Year and Date: 2016-08-01
  • Int'l Joint Research
• [Presentation] On some remarks of tight bounds for symmetric divergence measures (2016)
  • Author(s): Shigeru Furuichi, Kenjiro Yanagi and Ken Kuriyama
  • Organizer: 36th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering
  • Place of Presentation: Ghent(Belgium)
  • Year and Date: 2016-07-10
  • Int'l Joint Research
• [Presentation] Lowner微分方程式の普遍被覆写像への拡張 (2015)
  • Author(s): Hiroshi Yanagihara
  • Organizer: 等角写像論・値分布論研究集会
  • Place of Presentation: 山口大学(山口県・山口市)
  • Year and Date: 2015-12-05
  • Int'l Joint Research
• [Presentation] Generalized trace ineqalities related to fidelity and trace distance (2015)
  • Author(s): Kenjiro Yanagi
  • Organizer: The Seventh International Conference on INFORMATION
  • Place of Presentation: Taipei(Taiwan)
  • Year and Date: 2015-11-25
  • Int'l Joint Research
• [Presentation] On the trace inequalities of left-right multiplication operators (2015)
  • Author(s): Kenjiro Yanagi
  • Organizer: 2015実解析学シンポジウム
  • Place of Presentation: 東邦大学(千葉県・船橋市)
  • Year and Date: 2015-10-23
  • Int'l Joint Research
• [Presentation] 忠実度とトレース距離に関連した不等式の一般化について (2015)
  • Author(s): Kenjiro Yanagi
  • Organizer: 日本数学会函数解析学分科会
  • Place of Presentation: 京都産業大学(京都府・京都市)
  • Year and Date: 2015-09-13
• [Presentation] Generalized quasi-metric adjusted skew information and trace inequality (2015)
  • Author(s): Kenjiro Yanagi
  • Organizer: International Symposium on Banach and Function Spaces
  • Place of Presentation: 九州工業大学(福岡県・北九州市)
  • Year and Date: 2015-09-02
  • Int'l Joint Research
• [Presentation] Two points distribution estimates for convex univalent functions (2015)
  • Author(s): Mari Okada
  • Organizer: 等角写像論・値分布論合同研究集会
  • Place of Presentation: 幕張メッセ国際会議場(千葉市)
  • Year and Date: 2015-02-08
• [Presentation] ハイゼンベルグ及びシュレディンガー型の不確定性関係と非エルミート拡張について (2015)
  • Author(s): Kohei Sekikawa
  • Organizer: 日本数学会中四国支部例会
  • Place of Presentation: 徳島大学(徳島市)
  • Year and Date: 2015-01-25
• [Presentation] 歪情報量に付随した一般化不確定性関係について (2015)
  • Author(s): Minato Tomonari
  • Organizer: 日本数学会中四国支部例会
  • Place of Presentation: 徳島大学(徳島市)
  • Year and Date: 2015-01-25
• [Presentation] On a class of universal covering mappings (2014)
  • Author(s): Hiroshi Yanagihara
  • Organizer: International Conference on Geometric Function Theory
  • Place of Presentation: IIT Kharagpur, India(インド)
  • Year and Date: 2014-12-18 – 2014-12-21
• [Presentation] 非エルミート型の不確定性関係とその応用 (2014)
  • Author(s): Kenjiro Yanagi
  • Organizer: 第37回情報理論とその応用シンポジウム
  • Place of Presentation: 宇奈月ニューオータニホテル(黒部市)
  • Year and Date: 2014-12-09 – 2014-12-12
• [Presentation] Non-hermitian extensions of Schrodinger type uncertainty relations (2014)
  • Author(s): Kenjiro Yanagi
  • Organizer: International Symposium on Information Theory and its Applications
  • Place of Presentation: Melbourne Convension & Exhibition Center(オーストラリア)
  • Year and Date: 2014-10-26 – 2014-10-29
• [Presentation] 非エルミート型の不確定性関係 (2014)
  • Author(s): Kenjiro Yanagi
  • Organizer: 日本数学会函数解析学分科会
  • Place of Presentation: 広島大学(東広島市)
  • Year and Date: 2014-09-25 – 2014-09-28
• [Presentation] Non-hermitian extension of the Heisenberg and Schrodinger uncertainty relations (2014)
  • Author(s): Kenjiro Yanagi
  • Organizer: The Forth Assian Conference on Nonlinear Analysis and Optimization
  • Place of Presentation: 国立台湾師範大学（台湾）
  • Year and Date: 2014-08-05 – 2014-08-09
• [Book] 詳解微分積分演習 (2016)
  • Author(s): 加藤幹雄，柳研二郎，三谷健一，高橋泰嗣
  • Total Pages: 288
  • Publisher: サイエンス社
• [Remarks] http://ds0.cc.yamaguchi-u.ac.jp/~yanagi/index.html