A STUDY FOR ESTABLISHING THE FOUNDATION OF QUANTUM CORDING THEOREMS

建立量子绳定理基础的研究

• 批准号: 18540141
• 负责人: WATANABE Noboru
• 金额: $ 2.57万
• 依托单位: Tokyo University of Science
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2006
• 资助国家: 日本
• 起止时间: 2006 至 2009
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-18540141/
• 关键词: 情報数理; 量子情報; 量子情報理論; 量子符号化の定理; 量子エントロピー; 量子チャネル; 量子通信理論; 力学的エントロピー; 量子通信路容量; 量子エンタングルメント

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 measuresIn 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 systemsA 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.

为了讨论量子系统中的编码定理，我们需要研究（1）基于量子系统动态熵的量子系统中相互熵（信息）的配方。我们将上述（1）和（2）集中在以下结果中。（1）对信息传输效率通过量子共同镜的效率进行研究的研究，在通信过程中，通道具有一个功能，可以将输入系统的状态传输到输出系统，而相互熵则通过通道从输入系统中正确地发送了信息的信息量。我研究了量子相互熵类型的测量，即Ohya相互熵，连贯的信息和Lindblad-Nielsen熵，我与嘈杂的光通道的这些措施进行了比较。我获得了这样的结果，即Ohya相互熵最适合讨论量子编码定理。（2）对量子系统的动态熵的数学研究，用于量子系统的量子系统试验对动态熵的量子系统（Kolmogorov-Sinai熵）（Kolmogorov-Sinai熵）（Connes-Stormer，Emch，Emch，Connes-Narnharnhhhhhhhhhhhhhhofrricirrricirrricirricirricirricirricirricirricirricirrirricirricirricirricirricirricirricirricirricirricirricirricirricirricirricirring，ColloriD of，kolmogorov-sinai熵） Ohya（复杂性），Accardi-Ohya-Watanabe（AOW），Kossakowski-Ohya-Watanabe（Kow）等。在这项研究中，根据KOW动力学熵的制定，我严格检查了量子动力学熵的性能，以计算挤压输入状态和嘈杂的光通道的广义AOW熵，并针对由量子Markov工艺组成的动力学系统。

项目成果

Note on efficiency of information transmission for quantum control communication process by using squeezed state

关于压缩态量子控制通信过程信息传输效率的注记

• 发表时间: 2009
• 期刊: The Proceedings of the 32nd Symposium on Information Theory and its Applications 32
• 作者: T.Jitsukawa;N.Watanabe
• 通讯作者: N.Watanabe

On Construction of quantum logical gate based on FTM gate

基于FTM门的量子逻辑门的构建

• 发表时间: 2006
• 期刊: The Proceedings of the Sumposium on Information Theory and its Applications 29
• 作者: 山中俊幸;渡邉 昇
• 通讯作者: 渡邉 昇

量子暗号と量子テレポーテーション -新たな情報通信プロトコル-

量子密码学与量子隐形传态-新信息通信协议-

• 发表时间: 2006
• 作者: 大矢雅則;渡邉 昇
• 通讯作者: 渡邉 昇

Note on Entropies in Quantum Processes

关于量子过程中的熵的注释

• 发表时间: 2009
• 期刊: QP-PQ Quantum Probability and White Noise Analysis, Quantum Bio-InformaticsII ; From Quantum Information to Bio-Informatics 24
• 作者: 米田量昭;渡邉昇;N. Watanabe;N. Watanabe
• 通讯作者: N. Watanabe

4ビームスプリッターゲートを用いた量子計算過程の定式化について

关于使用四个分束器门的量子计算过程的制定

• 发表时间: 2007
• 期刊: The Proceedings of the 30th Symposium on Information Theory and its Applications 30
• 作者: A. Kossakowski;M. Ohya;M. Miyashita and N. Watanabe;H. Kataoka and N. Watanabe;S. Saito and N. Watanabe;Y. Takase and N. Watanabe;Y. Koshikawa and N. Watanabe;R. Furukoshi and N. Watanabe
• 通讯作者: R. Furukoshi and N. Watanabe