2020 Fiscal Year Final Research Report
Information-Theoretical Study of Entanglement and Geometry in Quantum Systems
| Project/Area Number |
18K03474
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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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| Review Section |
Basic Section 13010:Mathematical physics and fundamental theory of condensed matter physics-related
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| Research Institution | Tohoku University (2020)
Sendai National College of Technology (2018-2019) |
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Principal Investigator |
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| Project Period (FY) |
2018-04-01 – 2021-03-31
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| Keywords | エンタングルメント / 情報幾何学 / 量子古典変換 / ホログラフィー原理 / くりこみ群 / 特異値分解 |
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| Outline of Final Research Achievements |
The duality (holographic principle) between quantum critical systems and classical general relativity is a very basic research subject that includes common issues in various physical fields. The main purpose of this research is to clarify this background from cross-disciplinary perspectives such as information geometry, mathematical physics, and condensed matter physics. To achieve this, I conducted research on two specific issues:(1) research to the functionality of singular value decomposition and holographic principles, and (2) construction of quantum classical correspondence by information geometry. In particular, regarding (1), it was found that the wave function can be restored and inferred from the singular value decomposition (principal component analysis) of the family information of the correlation function of the quantum system, and it is found that this result can contribute to the understanding of the mechanism of the quantum classical correspondence.
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| Free Research Field |
物性基礎論
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| Academic Significance and Societal Importance of the Research Achievements |
情報に関わる研究は現代の最重要テーマの一つである．AIや深層学習は現代技術社会における必須の技術であり，また量子コンピュータは国家的な戦略課題でもある．それと並行して，基礎科学の大きな革新である次世代物理学の構築にも量子情報理論の観点は本質的な役割を果たすと考えられている．本研究は極めて数理物理的な基礎研究ではあるものの，このような非常に広い視点から後者に貢献すべき堅実な研究成果であり，そこに学術的・社会的意義があると考えられる．
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