| 研究課題/領域番号 |
20K03746
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| 研究種目 |
基盤研究(C)
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| 配分区分 | 基金 |
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| 応募区分 | 一般 |
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| 審査区分 |
小区分12040:応用数学および統計数学関連
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| 研究機関 | 名古屋大学 |
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研究代表者 |
Buscemi F. 名古屋大学, 情報学研究科, 教授 (80570548)
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| 研究期間 (年度) |
2020-04-01 – 2024-03-31
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| 研究課題ステータス |
交付 (2022年度)
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| 配分額 *注記 |
4,290千円 (直接経費: 3,300千円、間接経費: 990千円)
2022年度: 1,430千円 (直接経費: 1,100千円、間接経費: 330千円)
2021年度: 1,430千円 (直接経費: 1,100千円、間接経費: 330千円)
2020年度: 1,430千円 (直接経費: 1,100千円、間接経費: 330千円)
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| キーワード | thermodynamic resources / information engine / quantum error-correction / quantum guesswork / communication channels / fluctuation relations / quantum entanglement / quantum thermodynamics / quantum channels / quantum information / resource theories / statistical comparison / statistical decision / statistical inference |
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| 研究開始時の研究の概要 |
Some well-known features of quantum theory, such as quantum entanglement and quantum coherence, have moved from being qualitative traits of the theory to becoming tangible resources, with the potential to unlock various novel tasks in computation and communication. Such a resource-theoretic viewpoint on quantum theory has recently become mainstream in quantum information sciences. This project aims to investigate quantum resource theories as problems of statistical decision and inference, bringing in tools and insights from operator algebra and mathematical statistics.
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| 研究実績の概要 |
During FY2022 many projects that had to be postponed due to the COVID pandemics have resumed and have resulted in various important works, directly related to this project. The research achievements in FY2022 comprise two published papers, 5 arXiv preprints, and 9 invited talks. In what follows I will report about papers that have been already published.
In the paper "Thermodynamic Constraints on Quantum Information Gain and Error Correction: A Triple Trade-Off" we explored the relationship between quantum error correction and quantum thermodynamics, and derived an upper bound on the measurement heat dissipated during the error-identification stage in terms of the Groenewold information gain. We also showed that under a set of physically motivated assumptions, this leads to a fundamental triple trade-off relation, which implies a trade-off between the maximum achievable fidelity of error-correction and the super-Carnot efficiency that heat engines with feedback controllers have been known to possess.
In the paper "Von Neumann's information engine without the spectral theorem" we explored the role of the spectral theorem in von Neumann's argument for obtaining the formula for the entropy of a quantum state. We showed that the role of the spectral theorem can be taken over by the operational assumptions of repeatability and reversibility. As a byproduct, we obtained the Groenewold information gain as a natural monotone for a suitable ordering of instruments, providing it with an operational interpretation valid in quantum theory and beyond.
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| 現在までの達成度 (区分) |
現在までの達成度 (区分)
2: おおむね順調に進展している
理由
Since the lifting of travel restrictions due to COVID, the research plan about quantum resource theories has resumed and some projects that were left to wait have been either completed or resumed at full speed. At the moment, I am working to collect the results obtained during FY 2022 into papers, presentations, and lectures for students.
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| 今後の研究の推進方策 |
The plan for FY 2023 is to summarize the projects finalized in FY 2022 into papers, research presentations, and lecture notes.
We will explore resource theories of quantum measurements. In particular, we will study the concept of "quantum incompatibility" and "measurement sharpness" from the point of view of general resource theories. Our aim is to solve some problems that have remained open in the literature. The first problem is due to the existence of two competing and inequivalent definitions for quantum incompatibility. Another problem is the lack of a clear understanding of the set of operations that do not increase the sharpness of a measurement.
We will also extend to non-commutative setting our work on the probabilstic and statistical foundations of thermodynamics and fluctuation theorems. This final part will complete some of the ideas that we put forth during the last fiscal year.
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