2017 Fiscal Year Research-status Report
Mathematical aspects of quantum statistical physics and quantum information theory
| Project/Area Number |
17K05267
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| Research Institution | Tohoku University |
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Principal Investigator |
HANSEN FRANK 東北大学, 高度教養教育・学生支援機構, 教授 (00600678)
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| Project Period (FY) |
2017-04-01 – 2020-03-31
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| Keywords | quantum information / statistical mechanics / convexity / trace function |
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| Outline of Annual Research Achievements |
This year’s research activities fall within the main purpose of the program as stated in the application.
1. We studied convexity or concavity of certain trace functions for the deformed logarithmic and exponential functions, and we obtained in this way new trace inequalities for deformed exponentials that may be considered as generalizations of Peierls-Bogolyubov's inequality. This work has applications in quantum statistical mechanics, quantum information theory, and in the theory of operator inequalities. We used these results to improve previously known lower bounds for the Tsallis relative entropy.
2. In another study we introduced the notion of Jensen-type maps and arrived at a complete characterization of these objects. These results complemented our much earlier work on Jensen’s operator inequality and led to a complete understanding of the qualitative differences between Davis’s inequality and Jensen’s operator inequality.
3. In addition, we have initiated research on a completely new type of operator means, the so-called hyper means. These objects play an important role in fundamental aspects of quantum mechanics and quantum information theory. We hope to be able to advance this line of research to the extent that it may be published in time for next year’s report.
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| Current Status of Research Progress |
Current Status of Research Progress
2: Research has progressed on the whole more than it was originally planned.
Reason
This year’s research activities fall within the main purpose of the program as stated in the application, and the obtained results have been published in recognized international scientific journals and presented at international meetings and conferences.
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| Strategy for Future Research Activity |
We intend to continue the research program in accordance with the objectives laid out in the research plan mentioned in the application.
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Research Products
(4 results)
