Statistical Inference of Quantum Measurements
Project/Area Number |
20K03774
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Research Category |
Grant-in-Aid for Scientific Research (C)
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Allocation Type | Multi-year Fund |
Section | 一般 |
Review Section |
Basic Section 13010:Mathematical physics and fundamental theory of condensed matter physics-related
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Research Institution | Kyoto University |
Principal Investigator |
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Project Period (FY) |
2020-04-01 – 2024-03-31
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Project Status |
Granted (Fiscal Year 2022)
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Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2023: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2022: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2021: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2020: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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Keywords | data-driven inference / statistical inference / quantum inference / quantum measurement / quantum design / quantum measurements / quantum devices / machine learning / regular simplices / SIC measurements |
Outline of Research at the Start |
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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Outline of Annual Research Achievements |
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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Current Status of Research Progress |
Current Status of Research Progress
2: Research has progressed on the whole more than it was originally planned.
Reason
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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Strategy for Future Research Activity |
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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Report
(3 results)
Research Products
(13 results)