2009 Fiscal Year Final Research Report
A STUDY FOR ESTABLISHING THE FOUNDATION OF QUANTUM CORDING THEOREMS
| Project/Area Number |
18540141
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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 |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Tokyo University of Science |
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Principal Investigator |
WATANABE Noboru Tokyo University of Science, 理工学部, 教授 (70191781)
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| Co-Investigator(Renkei-kenkyūsha) |
OHYA Masanori 東京理科大学, 理工学部, 教授 (90112896)
SATO Keiko 東京理科大学, 理工学部, 講師 (30366439)
IRIYAMA Satoshi 東京理科大学, 理工学部, 助教 (10385528)
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| Project Period (FY) |
2006 – 2009
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| Keywords | 情報数理 / 量子情報 |
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| Research Abstract |
In order to discuss coding theorems in quantum systems, we need to investigate (1) a formulation of mutual entropy (information) in quantum systems and (2) a formulation of mean mutual entropy based on dynamical entropy of quantum system. We focus the above (1) and (2), and we obtained the following results.
(1)A study on efficiency of information transmission by means of quantum mutualentropy type measures
In a communication process, a channel has a function to transmit a state of the input system to output system, and the mutual entropy expresses the amount of information correctly sent output system from input system through a channel. I studied the quantum mutual entropy type measures, that is Ohya mutual entropy, coherent information and Lindblad- Nielsen entropy and I compared with these measures for the noisy optical channel. I obtained the result that Ohya mutual entropy is most suitable one for discussing the quantum coding theorems.
(2) A mathematical study of dynamical entropies for quantum systems
A trial of extension to quantum system of dynamic entropy (Kolmogorov-Sinai entropy) of classical system was studied by Connes-Stormer, Emch, Connes-Narnhofer-Thirring (CNT), Alicki-Fannes (AF), Ohya (Complexity), Accardi-Ohya-Watanabe (AOW), Kossakowski-Ohya-Watanabe(KOW), and so on. In this study, based on the formulation of KOW dynamical entropy, I strictly examined about the performance of the quantum dynamical entropy to calculate the generalized AOW entropy for the squeezed input state and the noisy optical channel, and for the dynamical system consisted of the quantum Markov process.
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