2007 Fiscal Year Final Research Report Summary
Study of Inequalities in Operator Theory and Quantum Information Theory
| Project/Area Number |
18540182
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Yamaguchi University |
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Principal Investigator |
KURIYAMA Ken Yamaguchi University, Graduate School of Science and Engineering, Professor (10116717)
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| Co-Investigator(Kenkyū-buntansha) |
YANAGI Kenjiro Yamaguchi University, Graduate School of Science and Engineering, Professor (90108267)
MATSUNO Yoshimasa Yamaguchi University, Graduate School of Science and Engineering, Professor (30190490)
YANAGIHARA Hiroshi Yamaguchi University, Graduate School of Science and Engineering, Associate professor (30200538)
OKADA Mari Yamaguchi University, Graduate School of Science and Engineering, Associate Professor (40201389)
NISHIYAMA Takahiro Yamaguchi University, Graduate School of Science and Engineering, Associate Professor (60333241)
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| Project Period (FY) |
2006 – 2007
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| Keywords | operator / quantum computation / Tsallis entropy / operator inequality / Cramer-Rao inequality / uncertainty relation / Heisenberg inequality / skew information |
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| Research Abstract |
1. Shannon entropy, von Neumann entropy, Umegaki entropy and Fujii-Kamei relative operator entropy are important in information theory. We extended them to operators in Hilbert spaces by using ideas of Tsallic entropy which is recently important in physics. Some properties sund as operator inequalities and trace inequalities were investigated.
2. Studies of algorithms of quantum computers, in particular, computational complexity are interesting. We gave precise estimation of Shor's factoring algorithm by using elementary number theory.
3. It is an important problem to study the relation between uncertainty relations in quantum physics and quantum information theory. We investigated an uncertainty relation by generalizing Wigner-Yanase skew information.
4. Introducing generalized Fisher information which is a trace of operator, we showed a generalized Cramer-Rao inequality which is important in statistics.
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