关于不确定性关系的若干研究

发布时间：2018-04-29 17:22

本文选题：Wigner-Yanase-Dyson斜信息 + 密度算子　；参考：《陕西师范大学》2015年硕士论文

【摘要】：Heisenberg不确定性关系是量子力学和量子信息中的重要内容,也是数学和信息论中的一个热点问题.本文以量子力学理论为背景,综合运用分析、代数的思想方法,以算子代数、算子理论和矩阵分析等为工具运用信息论的知识,通过系统地研究Heisenberg不确定性关系,把Heisenberg不确定性关系推广到Hilbert-Schmidt算子,证明了广义的Heisenberg不确定性关系.最后研究了广义的Wigner-Yanase斜信息,讨论了其性质,并证明了一些迹类不等式.本文分为三章,具体结构如下：第1章介绍了本文研究的背景意义和现状,并引入了一些最基本的概念,指出了本文研究的方向.第2章研究了广义的Heisenberg不确定性关系.首先,介绍了Hilbert-Schmidt算子、对称交换子、对称反交换子、斜信息和关联量等概念；然后,证明了广义的Heisen-berg不确定性关系及其推广形式.第3章首先引入广义的Wigner-Yanase斜信息的定义,然后讨论了其性质,并证明了一些迹类不等式.
[Abstract]:Heisenberg uncertainty relation is an important content in quantum mechanics and quantum information, and it is also a hot issue in mathematics and information theory. In this paper, based on the theory of quantum mechanics, using the analytical and algebraic thinking methods, using operator algebra, operator theory and matrix analysis as tools, we systematically study the uncertain relation of Heisenberg by using the knowledge of information theory. The Heisenberg uncertainty relation is extended to the Hilbert-Schmidt operator and the generalized Heisenberg uncertainty relation is proved. Finally, the generalized Wigner-Yanase oblique information is studied, its properties are discussed, and some trace class inequalities are proved. This paper is divided into three chapters, the concrete structure is as follows: chapter 1 introduces the background significance and present situation of this paper, introduces some basic concepts, and points out the research direction of this paper. In chapter 2, the generalized Heisenberg uncertainty relation is studied. Firstly, the concepts of Hilbert-Schmidt operator, symmetric commutator, symmetric inverse commutator, oblique information and correlation quantity are introduced, and then the generalized Heisen-berg uncertainty relation and its generalized form are proved. In chapter 3, we first introduce the definition of generalized Wigner-Yanase oblique information, then discuss its properties and prove some trace class inequalities.
【学位授予单位】：陕西师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O177

【参考文献】