| 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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| 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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