Project/Area Number |
16F16702
|
Research Category |
Grant-in-Aid for JSPS Fellows
|
Allocation Type | Single-year Grants |
Section | 外国 |
Research Field |
Foundations of mathematics/Applied mathematics
|
Research Institution | Kyoto University |
Principal Investigator |
宮寺 隆之 京都大学, 工学研究科, 准教授 (50339123)
|
Co-Investigator(Kenkyū-buntansha) |
HAAPASALO ERKKA 京都大学, 工学(系)研究科(研究院), 外国人特別研究員
|
Project Period (FY) |
2016-07-27 – 2018-03-31
|
Project Status |
Completed (Fiscal Year 2017)
|
Budget Amount *help |
¥1,500,000 (Direct Cost: ¥1,500,000)
Fiscal Year 2017: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2016: ¥800,000 (Direct Cost: ¥800,000)
|
Keywords | quantum measurement / Quantum Theory / Quantum Measurement |
Outline of Annual Research Achievements |
We study positive kernels on X×X, where X is a set equipped with an action of a group, and taking values in the set of A-sesquilinear forms on a (not necessarily Hilbert) module over a C*-algebra A. These maps are assumed to be covariant with respect to the group action on X and a representation of the group in the set of invertible (A-linear) module maps. We find necessary and sufficient conditions for extremality of such kernels in certain convex subsets of positive covariant kernels. Our focus is mainly on a particular example of these kernels: a completely positive (CP) covariant map for which we obtain a covariant minimal dilation (or KSGNS construction). We determine the extreme points of the set of normalized covariant CP maps and, as a special case, study covariant quantum observables and instruments whose value space is a transitive space of a unimodular type-I group. As an example, we discuss the case of instruments that are covariant with respect to a square-integrable representation.
|
Research Progress Status |
29年度が最終年度であるため、記入しない。
|
Strategy for Future Research Activity |
29年度が最終年度であるため、記入しない。
|