2022 Fiscal Year Research-status Report
Statistical Inference of Quantum Measurements
| Project/Area Number |
20K03774
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| Research Institution | Kyoto University |
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Principal Investigator |
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| Project Period (FY) |
2020-04-01 – 2024-03-31
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| Keywords | data-driven inference / statistical inference / quantum inference / quantum measurement / quantum design |
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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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| Causes of Carryover |
The grant will be used for conducting research. In particular, this included basic laboratory electronic equipment and business trips to disseminate the scientific results obtained.
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