Mathematical study on quantum incompatibility
| Project/Area Number |
15K04998
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
Foundations of mathematics/Applied mathematics
|
|---|
| Research Institution | Kyoto University |
|---|
Principal Investigator |
|
|---|
| Project Period (FY) |
2015-04-01 – 2020-03-31
|
| Project Status |
Completed (Fiscal Year 2019)
|
| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2018: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
|
|---|
| Keywords | 量子論基礎 / 量子情報 / 量子確率 / 量子測定 / 両立不可能性 / 不確定性関係 / 一般確率論 |
|---|
| Outline of Final Research Achievements |
We studied quantum incompatibility with focus on its structural aspect. We showed that order relations in observable space and quantum channel space are naturally introduced and the incompatibility is represented in a simple way by using these relations. The argument was extended to the incompatibility between quantum channels. In addition, we generalized the notion so that compatibility between subsets can be treated. For a given subset in the observable space, we have a subset in the channel space such that each element in this channel space is compatible with every element in the observable subset. This treatment naturally introduced the Galois connection, whose closure is shown to have an operational interpretation. We also studied the incompatibility witness whose existence is derived from the convex structure of the set of all compatible pairs. As applications of the quantum incompatibility, we investigated the quantum reference frame and obtained some quantitative bounds.
|
| Academic Significance and Societal Importance of the Research Achievements |
位置と運動量が同時に測定できないという不確定性関係は量子論において最も長い歴史をもつにもかかわらず、いまだにその定式化においてすら混乱が見られ、その全貌は解き明かされていません。この定式化を数学的に操作論的に満足のいく形で行い、また位置と運動量の測定にとどまらず一般的な操作にまで概念を拡張したものが同時操作不可能性です。この研究では、同時操作不可能性について、その根本的な理由を探るべく構造論的観点から調べました。また、この概念がどのように応用されるかについても調べました。これは量子情報など「役に立つもの」への応用につながるものと考えています。
|
Report
(6 results)
Research Products
(30 results)
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
[Journal Article] An Invitation to Quantum Incompatibility2016
Author(s)
Teiko Heinosaari, Takayuki Miyadera, Mario Ziman
-
Journal Title
Journal of Physics A: Mathematical and Theoretical
Volume: 49
Issue: 12
Pages: 123001-123001
DOI
Related Report
Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
-
-
-
-
-
-
