2017 Fiscal Year Annual Research Report
量子論における同時操作不可能性とその順序構造による特徴づけ
| Project/Area Number |
16F16702
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| Research Institution | Kyoto University |
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Principal Investigator |
宮寺 隆之 京都大学, 工学研究科, 准教授 (50339123)
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| 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
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| Project Period (FY) |
2016-07-27 – 2018-03-31
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| Keywords | quantum measurement |
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| 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.
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| Research Progress Status |
29年度が最終年度であるため、記入しない。
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| Strategy for Future Research Activity |
29年度が最終年度であるため、記入しない。
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