| 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 – 2025-03-31
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| 研究課題ステータス |
交付 (2023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 | quantum measurements / quantum instruments / quantum incompatibility / measurement sharpness / 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 FY2023, two very important papers for this project were finally published. One is the paper: "Unifying different notions of quantum incompatibility into a strict hierarchy of resource theories of communication" and the other is: "A complete and operational resource theory of measurement sharpness". These papers lay the foundations for a coherent resource-theoretic characterization of quantum measurement processes. The first paper deals with the notion of incompatibility, which was clear for POVMs but was hotly debated in the case of instruments, and finally settles the situation by introducing an overarching framework to unify and harmonize pervious proposals. The second paper instead deals with the notion of sharpness, which we relate to the operational idea of repeatability. Moreover, a coherent framework for sharpness-non-increasing operations, something that other researchers have been looking for in the past, has been finally obtained. In addition, another resource-theoretic result was obtained: "Generalized resource theory of purity: one-shot purity distillation with local noisy operations and one way classical communication". The resource theory of purity plays an important role in modern formulations of quantum thermodynamics, and here we study the case of two players cooperating in the task.
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| 現在までの達成度 (区分) |
現在までの達成度 (区分)
1: 当初の計画以上に進展している
理由
The number of papers published this year is particularly high (see later). Among these, three papers were among the main goals of the present project, and all of them have been published in good journals.
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| 今後の研究の推進方策 |
This project has been extended for another year. The reason is that the final journal paper of "Generalized resource theory of purity: one-shot purity distillation with local noisy operations and one-way classical communication" is still in preparation. (Currently only a proceeding version has been published.) The remaining funds will be used to facilitate the international collaboration on which this paper is based.
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