关于有界线性算子斜信息的若干研究

发布时间：2018-02-05 00:36

本文关键词： Wigner-Yanase-Dyson斜信息交换子密度算子不确定关系方差协方差　出处：《陕西师范大学》2015年硕士论文　论文类型：学位论文

【摘要】：量子力学是现在物理学的理论支柱之一.著名物理学家Winger和Yanase在研究量子测量理论时提出了量子信息论的概念.本文在量子信息论的基础上运用代数、分析等思想方法,研究了含两个参数的广义Wigner-Yanase-Dyson斜信息及其相关性质,并给出了两个系统下自伴算子的斜信息、方差、协方差和相关测量与一个系统下这些量的关系.最后,研究了斜信息强可加性的相关问题.本文分为三章,具体结构如下：第一章,介绍了本文的研究意义以及研究现状,并引入了一些基本的概念和定理.第二章,首先介绍了含两个参数的广义Wigner-Yanase-Dyson斜信息的相关基本概念.其次,探讨了其相关性质并加以证明.最后,给出了Schrodinger不确定性关系的推广及其证明.第三章,研究了单系统中自伴算子的斜信息、方差、协方差和相关测量与复系统下这些量的关系.首先给出了斜信息、方差、协方差和相关测量的概念.其次,给出了其相关可加性及其证明,并提出了一个猜想,给出了相关例子.最后,研究了斜信息强可加性的相关问题.
[Abstract]:Quantum mechanics is one of the theoretical pillars of physics today. Famous physicists Winger and Yanase put forward the concept of quantum information theory while studying quantum measurement theory. Using algebra. In this paper, we study the generalized Wigner-Yanase-Dyson skew information with two parameters and its related properties, and give the skew information and variance of the self-adjoint operator under two systems. The relationship between covariance and correlation measurement and these quantities under a system. Finally, we study the correlation problem of strong additivity of oblique information. This paper is divided into three chapters, the specific structure is as follows: chapter 1. This paper introduces the research significance and research status, and introduces some basic concepts and theorems. Chapter two. Firstly, the basic concepts of generalized Wigner-Yanase-Dyson oblique information with two parameters are introduced. Secondly, its properties are discussed and proved. In chapter 3, the skew information and variance of self-adjoint operator in single system are studied. First, the concepts of skew information, variance, covariance and correlation measurement are given. Secondly, the correlation additivity and its proof are given, and a conjecture is put forward. Finally, we study the strong additivity of oblique information.
【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;O413.1

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