Matrix/operator analysis (inequalities, mean, majorization) and applications to quantum information
| Project/Area Number |
17K05266
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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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| Project Period (FY) |
2017-04-01 – 2021-03-31
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| Project Status |
Completed (Fiscal Year 2020)
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| Budget Amount *help |
¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥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 / 作用素平均 / 量子情報理論 / 関数解析 / 行列 / 作用素環 / 量子情報 |
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| Outline of Final Research Achievements |
Matrix/operator analysis has played an imprtant role in quantum information theory that has intensively developed in recent years. In the course of this research project, toward applications to quantum information, we studied various problems related to matrix/operator analysis from the point of view of inequalities and obtained many results in different related subjects. Concerned with problems in matrix/operator analysis itself, we studied various inequalities, operator means of two-variables and several variables, and majorizations for matrices and operators, in relation to each other. As for quantum information, applying techniques from matrix/operator analysis, we studied monotonicity and reversibility under quantum channels for several types of quantum divergences.
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| Academic Significance and Societal Importance of the Research Achievements |
行列・作用素解析の研究では関数解析的な考え方が基本であるが，本研究ではリーマン幾何からのアイデア，確率論を使う手法，量子情報理論との相互乗り入れなど，多面的な考え方と方法論を駆使したところに，学術的意義と特色がある．本研究の研究成果を適宜，内外の数学専門雑誌に発表することにより，数学の国際コミュニティーへの発信を通して社会に寄与することができた．特に，本研究期間中に，フォン・ノイマン環と量子ダイバージェンスに関する２冊のモノグラフをヨーロッパ数学会とシュプリンガー社から出版したことで，これらの分野の発展に貢献できた．
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Report
(5 results)
Research Products
(47 results)
