2020 Fiscal Year Research-status Report
Statistical Inference of Quantum Measurements
| Project/Area Number |
20K03774
|
|---|
| Research Institution | Kyoto University |
|---|
Principal Investigator |
|
|---|
| Project Period (FY) |
2020-04-01 – 2024-03-31
|
| Keywords | statistical inference / machine learning / quantum measurements / regular simplices / SIC measurements |
|---|
| Outline of Annual Research Achievements |
The statistical inference of quantum measurements have been introduced, and its mathematical properties, such as the uniqueness of the output of the inference, have been studied. The same properties have been analyzed for generalized probabilistic theories, thus singling out the peculiarities of quantum theory with respect to the statistical inference of measurements. The input correlations for which the statistical inference produces the correct output have been characterized, thus providing a new operational interpretation to regular simplices in the quantum state space (also known as symmetric, informationally complete structures). Some of the results have been extended to the related problem of the statistical inference of quantum states.
|
| 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 project is proceeding smoothly, and has been fostered by domestic and international collaborations.
|
| Strategy for Future Research Activity |
Analytical results on the computation of the statistical inference of quantum measurements will be derived for the arbitrary dimensional case. The characterization of the input correlations for which the statistical inference produces the correct otuput quantum measurements will be extended to encompass the case of arbitrary number of outcomes. Parallel results for the problem of the statistical inference of quantum states will also be investigated. A protocol for the machine learning of quantum measurements based on their statistical inference will be implemented on the IBM quantum computer, and applied to other related problems such as quantum tomographic reconstruction.
|
| Causes of Carryover |
The amount allocated for the fiscal year 2021 will be mainly used to financially support business visits to collaborators of the project.
|
