Trace functionals and operator inequalities with applications in quantum information
Project/Area Number |
26400104
|
Research Category |
Grant-in-Aid for Scientific Research (C)
|
Allocation Type | Multi-year Fund |
Section | 一般 |
Research Field |
Basic analysis
|
Research Institution | Tohoku University |
Principal Investigator |
Frank Hansen 東北大学, 高度教養教育・学生支援機構, 教授 (00600678)
|
Project Period (FY) |
2014-04-01 – 2017-03-31
|
Project Status |
Completed (Fiscal Year 2016)
|
Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
|
Keywords | 量子情報 / Golden Thompson's ineq. / Quantum information / Statistical mechanics / Quantum entropy / geometric means / Rao's inequality / quantum entropy / GT-inequality / regular operator map / geometric mean / perspective / operator inequality / partial trace / Golden Thompon's ineq. / matrix entropy / trace inequality / regular operator mapping / concave trace function |
Outline of Final Research Achievements |
We found a multivariate extension of Golden-Thompson’s trace inequality, which may be considered as an interpolation inequality between Golden-Thompson’s inequality and Jensen’s inequality, and we extended the two variable Golden-Thompson inequality to deformed exponentials. We proposed a general procedure to construct multivariate geometric means based on the theory of perspectives of regular operator maps. The method is general enough to encompass all known examples of multivariate geometric means, and it also provides new interesting examples. A novel feature is that we may impose an updating procedure adapted to data acquisition. We characterised the von Neumann entropy as the only possible entropic measure satisfying two fundamental properties coming from thermodynamics. We obtained an inequality for expectations of means of positive random variables.
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Report
(4 results)
Research Products
(18 results)