量子信息处理中的信息度量与关联问题研究

项目名称： 量子信息处理中的信息度量与关联问题研究

项目编号： No.11461045

项目类型： 地区科学基金项目

立项/批准年度： 2015

项目学科： 数理科学和化学

项目作者： 吴照奇

作者单位： 南昌大学

项目金额： 36万元

中文摘要： 量子信息度量与量子关联是量子信息论的重要研究内容，在各种信息处理问题中发挥着巨大作用。在申请人前期相关工作的基础上，本项目拟研究如下问题：首先，定义量子操作间的新度量, 通过算子矩阵分块技巧讨论其性质；研究部分保真度以及基于部分保真度的关联矩阵的界估计；利用投影逼近方法进一步将这些结果推广到无穷维情形。其次，引入新的两体和多体量子关联度量，讨论其刻画与计算，得到关于不同类型量子态的解析表达式；构建量子关联与非局域性及广义不确定性原理之间的关系；研究不同环境下量子关联的动力学演化。最后，结合锥理论和凸分析的方法，在广义概率论框架下探讨各种信息度量以及不同条件下的信息转移问题。

中文关键词： 信息度量；量子关联；量子测量；动力学演化；广义概率论

英文摘要： Quantum information measure and quantum correlation are both important topics in quantum information theory, which play an indispensable role in various information processing tasks. Based on our previous work, in this project,we intend to further study the following problems: First of all, we will give some new metrics between quantum operations, and use operator block techniques to discuss their properties; we will study the bound estimation of partial fidelity and correlation matrix based on partial fidelity; we will then use projection approximation method to further generalize these results to infinite-dimensional case. Secondly, we will introduce some new measures of bipartite and multipatite quantum correlations,discuss their characterizations and calculations,and obtain the analytical expressions for different types of quantum states; we will try to establish the relationship between quantum correlation, nonlocality and generalized uncertainty relation; Meanwhile,we will devote to studying the dynamic evolution of quantum correlations in different enviroments. Finally, we propose to investigate various information measures and informaton transfer problems under different conditions in the framework of general probabilistic theories by combining cone theory and the methods in convex analysis.

英文关键词： information measure;quantum correlation;quantum measurement;dynamic evolution;general probabilistic theory