Mathematical studies on quantum entropy and its applications to information science
Project/Area Number |
24540146
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Research Category |
Grant-in-Aid for Scientific Research (C)
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Allocation Type | Multi-year Fund |
Section | 一般 |
Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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Research Institution | Nihon University |
Principal Investigator |
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Project Period (FY) |
2012-04-01 – 2016-03-31
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Project Status |
Completed (Fiscal Year 2015)
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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.
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Report
(5 results)
Research Products
(31 results)
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[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
Invited
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