本文選題：Wigner-Yanase-Dyson斜信息 + 密度算子��； 參考：《陜西師范大學(xué)》2015年碩士論文

【摘要】：Heisenberg不確定性關(guān)系是量子力學(xué)和量子信息中的重要內(nèi)容,也是數(shù)學(xué)和信息論中的一個(gè)熱點(diǎn)問題.本文以量子力學(xué)理論為背景,綜合運(yùn)用分析、代數(shù)的思想方法,以算子代數(shù)、算子理論和矩陣分析等為工具運(yùn)用信息論的知識(shí),通過系統(tǒng)地研究Heisenberg不確定性關(guān)系,把Heisenberg不確定性關(guān)系推廣到Hilbert-Schmidt算子,證明了廣義的Heisenberg不確定性關(guān)系.最后研究了廣義的Wigner-Yanase斜信息,討論了其性質(zhì),并證明了一些跡類不等式.本文分為三章,具體結(jié)構(gòu)如下：第1章介紹了本文研究的背景意義和現(xiàn)狀,并引入了一些最基本的概念,指出了本文研究的方向.第2章研究了廣義的Heisenberg不確定性關(guān)系.首先,介紹了Hilbert-Schmidt算子、對(duì)稱交換子、對(duì)稱反交換子、斜信息和關(guān)聯(lián)量等概念；然后,證明了廣義的Heisen-berg不確定性關(guān)系及其推廣形式.第3章首先引入廣義的Wigner-Yanase斜信息的定義,然后討論了其性質(zhì),并證明了一些跡類不等式.
[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.
【學(xué)位授予單位】：陜西師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類號(hào)】：O177

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本文編號(hào)：1820866