Matrix/operator inequalities and applications to quantum information and free probability
| Project/Area Number |
26400103
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Tohoku University |
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Principal Investigator |
Hiai Fumio 東北大学, 情報科学研究科, 名誉教授 (30092571)
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| Research Collaborator |
UEDA YOSHIMICHI 九州大学, 大学院数理学研究院, 准教授
Bourin Jean-Christophe Universite de Franche Comte
Ruskai M. B. University of Massachusetts Lowell, Emeritus Professor
Audenaert K. M. R. Royal Holloway, University of London
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 関数解析学 / 作用素 / 行列解析 / 作用素環 / 量子情報 / 自由確率論 / 作用素平均 |
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| Outline of Final Research Achievements |
In the course of this research project we obtained various results in the three subjects of matrix/operator analysis, quantum information, and free probability. In matrix/operator analysis, we studied the higher order extension, called k-tone functions, of operator momotone and concave functions in connection with the kth derivative of functional calculus. We introduced the notion of symmetric anti-norms for matrices/operators and discuseed the Jensen-Minkowski type cancavity and superadditivity inequalities of matrix trace/norm functions involving operator means and symmetric anti-norms. We also studied extensions of Araki's and Ando-Hiai's log-majorizations from different aspects.
In quantum information, we studied contraction coefficients for quantum channels with respect to quantum f-divergences and quantum monotone metrics. In free probability, we studied the orbital free entropy and free Fisher information from the viewpoint of variational principle based on Legendre transform.
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Report
(4 results)
Research Products
(30 results)
