研究課題/領域番号 |
20K03774
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研究種目 |
基盤研究(C)
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配分区分 | 基金 |
応募区分 | 一般 |
審査区分 |
小区分13010:数理物理および物性基礎関連
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研究機関 | 京都大学 |
研究代表者 |
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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 |
4,160千円 (直接経費: 3,200千円、間接経費: 960千円)
2023年度: 1,040千円 (直接経費: 800千円、間接経費: 240千円)
2022年度: 1,040千円 (直接経費: 800千円、間接経費: 240千円)
2021年度: 1,040千円 (直接経費: 800千円、間接経費: 240千円)
2020年度: 1,040千円 (直接経費: 800千円、間接経費: 240千円)
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キーワード | data-driven inference / statistical inference / quantum inference / quantum measurement / quantum design / quantum measurements / quantum devices / machine learning / regular simplices / SIC measurements |
研究開始時の研究の概要 |
This research plan will produce analytical and numerical results on the relevant problem of the statistical inference of quantum measurements. It will also produce implementations of quantum algorithms for the machine learning of quantum measurement with the IBM Q quantum computer.
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研究実績の概要 |
The statistical inferennce of quantum measurements recasts the problem of characterizing an unspecified measurement given an input-output correlations it has generated. In order to do so, a minimality criterion is adoppted according to which the minimally committal measurement should be inferred, among all measurements consistent with the correlation, in the sense of majorization theory and statistical comparison. After completing the characterization of the statistical inference of single qubit measurements in the previous years, I have explored the arbitrary dimensional case. I have shown that, in the general case, the statistical inference is equivalent to the quantum tomographic reconstruction if a spherical design set of states is assumed in the latter protocol. That is, while any informationally complete set of state can be assumed for tomographic reconstruction, not any informationally complete set is minimally committal in the sense defined by statistical inference. This clarifies the role of designs in the quantum statistical inference, with direct implications in interpretations of quantum theory such a s quantum Bayesianism, as well as in the study of designs and, generally, morphophoric measurements.
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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
The research is proceeding according to plan. I have produced papers published on international, peer reviewed journals and I have delivered presentations at international conferences.
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今後の研究の推進方策 |
For the FY2023, I plan to further explore the arbitrary dimensional case, in particular in relation to the applications of statistical inference to resource theories. In doing so, I will pave the way for a data-driven approach to quantum resource theories, statistical comparison, and majorization theory.
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