抄録
Offer Organization: Japan Society for the Promotion of Science, System Name: Grants-in-Aid for Scientific Research, Category: Grant-in-Aid for Scientific Research (C), Fund Type: competitive_research_funding, Overall Grant Amount: - (direct: 2500000, indirect: 750000)
In this project, we developed the general framework to analyze the parameter estimation problem when a quantum system of interest interacts with unknown environment. As the main result, we established the quantum estimation theory for quantum statistical models containing nuisance parameters. We extended the theory of optimal design of experiments to the more general setting such as quantum state and channel estimation problem. The proposed method were applied to find an optimal estimation strategy for quantum estimation problems in the presence of nuisance parameters. We characterized quantum statistical models based on the properties of tangent spaces. Our method aimed at unifying different choices of operator monotone metrics on the quantum state manifold in quantum information geometry. We applied our proposal to several examples in physical systems to illustrate effectiveness of our approach.