| Project/Area Number |
26800048
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Basic analysis
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| Research Institution | Kyoto University |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
Fukuda Motohisa 山形大学, 理学部, 准教授 (70771161)
Matsumoto Sho 鹿児島大学, 理工学域理学系, 准教授 (60547553)
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| Research Collaborator |
Brannan Michael Texas A&M University, Department of Mathematics
Zhong Ping University of Waterloo, Department of Mathematics
Dahlqvist Antoine University of Cambridge, Statlab
Kemp Todd University of California San Diego
Nechita Ion CNRS
Hyden Patrick Stanford University, Physics Department
Gaudreau Lamarre Princeton University
Pierre Yves Princeton University
Kousha Termeh University of Ottawa, Departement of Mathematics and Statistics
Kulik Rafal University of Ottawa, Departement of Mathematics and Statistics
Szarek Tomasz University of Gdansk, Department of Mathematics
Życzkowski Karol Jagiellonian University, Institute of Physics
Szymański Konrad Jagiellonian University, Institute of Physics
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | Random matrices / quantum information / random matrix theory / representation theory / Random Matrices / Quantum Information / MOE additivity / positive maps / Connes Problem / free probability / planar algebras / Ramdom matrices / free quantum groups / Weingarten formula |
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| Outline of Final Research Achievements |
In this research project, we investigated random matrices, which are matrices with random elements, via the moment method. Especially, we developed so-called Weingarten calculus and applied it to random matrix models which appear in quantum information theory.
For example, we gave a new approach to the problem of violation for the additivity of the minimum output entropy and obtained new examples in the problem of entanglement detection. These problems are quite
important problems in quantum information theory.
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