| 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 |
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| 応募区分 | 一般 |
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| 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 | 豊橋技術科学大学 (2023)
京都大学 (2020-2022) |
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研究代表者 |
DALLARNO Michele 豊橋技術科学大学, 工学(系)研究科(研究院), 准教授 (50870052)
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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 |
4,160千円 (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 | statistical inference / quantum measurements / 2 designs / testing regions / Lorenz curve / conical approximations / John ellipsoid / data-driven inference / quantum inference / quantum measurement / quantum design / quantum devices / machine learning / regular simplices / SIC measurements |
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| 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 |
In the FY2023, I generalized my previous results on the statistical inference of quantum measurements, that were restricted to the qubit case, to the arbitrary dimensional case. This could be achieved by first characterizing inner and outer conical approximations of the range of arbitrary dimensional quantum measurements. Such approximations are tight, that is, they are maximal and minimal in volume among all conical approximatins, and are close, that is, the one is transformed into the other by a constant rescaling. I showed that any measurement that produces a given set of conditional probability distributions upon the input of a 2-design set of states, maximizes the Bayesian posterior probability distribution in the inferential process. I also showed how to apply the aforementioned results to the device independent testing of the statistical sufficiency of quantum measurements. I presented my results in 21 presentations, including keynote and invited speeches in international conferences including the Analytical and Combinatorial Methods in Quantum Information Thoery II (Edinburgh, UK, July 2023), Quantum Foundation workshop (Graz, Austria, August 2023), and ICAICTA (Lonbok, Indonesia, October 2023).
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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 project is progressing smoothly. Several papers have been published by me and collaborators on the topic.
M. Dall'Arno, F. Buscemi, T. Koshiba, Computing the quantum guesswork: a quadratic assignment problem, QIC 23, 0721 (2023); M. Dall'Arno, On the Measurement attaining the Quantum Guesswork, IEEE Trans. Inform. Theory 70, 2713 (2024); B. Avirmed, K. Niinomi, M. Dall'Arno, Adversarial guesswork with quantum side information, QIC 23, 1105 (2023)
M. Dall'Arno, On the role of designs in the data-driven approach to quantum statistical inference, arXiv:2304.13258; M. Dall'Arno, F. Buscemi, Tight conic approximation of testing regions for quantum statistical models and measurements, arXiv:2309.16153; M. Dall'Arno, A. Tosini, F. Buscemi, The signaling dimension in generalized probabilistic theories, arXiv:2311.13103
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| 今後の研究の推進方策 |
The natural development of the present research project is in the device-independent approach to quantum resource theories. On the one hand, the device-independent approach to Quantum Theory dictates that experimental results should be interpreted without any assumption on the devices involved, and accordingly allows for the theory itself to be tested. On the other hand, the resource-theoretical approach to Quantum Theory is based on establishing a hierarchy among devices based on the ability of some devices to simulate other devices. I plan to extend and unify these two approaches, that so far have separately drawn a considerable interest by two distinct communities. To this aim, I will overcome many of the limitations of the state of the art in each field, in particular by
extending known results beyond the binary and two-dimensional case. As a result, I will
show how to certify, in a device-independent way, whether any given quantum device is
able of simulating any other given device, thus establishing a device-independent
hierarchy among devices based on the simulability criterion.
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