2015 Fiscal Year Research-status Report
Trace functionals and operator inequalities with applications in quantum information
| Project/Area Number |
26400104
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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) |
2014-04-01 – 2017-03-31
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| Keywords | quantum entropy / partial trace / regular operator map / Golden Thompon's ineq. / matrix entropy |
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| Outline of Annual Research Achievements |
1. We arrived at final publication of our work on regular operator mappings with applications to multivariate geometric means. We continued the work on inequalities related to Golden-Thompson’s trace inequality and arrived at final publication of two papers related to this inequality. In one paper we explored extensions of the inequality, which is important in quantum statistical mechanics, to a multivariate setting. In another direction we published a paper extending the two variable Golden-Thompson inequality to deformed exponentials with parameters in the interval [1,3]. After much revision of earlier preprints we obtained final publication of our work about the characterization of matrix entropies. Most of the work mentioned in this section has been extensively communicated at various international conferences.
2. In addition to the completion of earlier work we opened up research in two new areas both connected to quantum information theory. We connected the earlier developed theory of regular operator mappings with the theory of partial traces and found many new applications in quantum information theory and quantum physics. We also reconsidered the von Neumann entropy and found a surprisingly simple proof of an important classical result by connecting it with the theory of matrix entropies. We finally initiated work on fundamental aspects of quantum entropy, but this line of research is too embryonic to be reported at this stage.
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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 is divided into two parts. The first part deals with the completion of work already developed in the first year of research, or earlier, and the work associated with final publication of these ideas in scientific journals. The second part is about new ideas and techniques developed in the second year of the research program. Both activities fall within the main purpose of the program as stated in the application.
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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.
In conjunction with this effort we have separate research programs with Paolo Gibilisco (Rome, Tor Vergata), Edward Effros (UCLA), Elliott Lieb (Princeton), Liang Cai (Beijing Institute of Technology) and Zhihua Zhang (Jiangsu University).
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| Causes of Carryover |
旅費の見込額との差異が生じたため。
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| Expenditure Plan for Carryover Budget |
次年度は国内外で行われる学会への参加および研究者との研究に関する協議等を行うための旅費や学会参加費として執行する予定。
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