【作者】 王进；

【导师】 景乃桓；

【作者基本信息】 华南理工大学 ， 基础数学， 2015， 硕士

【摘要】 不可扩展基(UPBs)在量子信息论中占据非常重要的地位,例如,利用不可扩展基(UPBs)构造边界纠缠态,和不可分的正定映射等.因而,有关不可扩展基的构造问题也得到了广泛的关注和研究并取得了大量的研究成果.基于此,本文研究了不可扩展基的几种构造方法.本文的第一章是绪论,主要介绍了不可扩展基的研究现状和本文的主要工作第二章主要介绍了有关不可扩展基的基础知识,介绍了希尔伯特空间及态矢,介绍了态矢的狄拉克符号表示和矩阵之间的关系及左矢和右矢之间的运算,并给出了希尔伯特空间上的一些常用算符及其运算,最后介绍了直积空间及其上的运算.第三章是本文的主要内容：介绍了不同qibit上不可扩展基的构造和两个重要的UPBs:GenTiles1,GenTiles2.在此基础上,本文做了以下几个方面的工作：首先,介绍了Cm×Cn上两种不同形式的U PBs;其次,构造了Cm×Cn上(n-1)2个态的UPBs;然后,用图形分析法构造了Cm×Cn上另一类(n-1)2个态和(n-1)2+1个态的U P Bs;]最后,介绍了Cm×Cn×Cs上 U P Bs的构造.更多还原

【Abstract】 Unextendible Product Bases(U P Bs) occupy an important position in the theory of quantum information, for example, they were introduced as a tool for constructing bound entangled states, they can also be used to construct indecomposible positive maps. Therefore, the problems of UPBs.structure have been widespreadly concerned and a large number of results have been researched. Based on these researches, several methods of the construction of the U P Bs are researched in this paper.The first chapter is the introduction, in which the research status of the unextendible product bases and the main work of this paper are mainly introduced.The basics of U P Bs are mainly introduced in the second chapter, including the Hilbert space, state vector, the representation of state vector of Dirac’s symbolic operations, the relationship of the matrices,and the operations between left and right vectors.Then, some commonly used operators and its operation in Hilbert space are introduced.Finally, the direct product space and its operations are presented.The third chapter is the main content of this paper: the construction of U P Bs in di?erent qubit and two important U P Bs are provided, including Gen Tiles1, GenTiles2. This thesis focuses on the following works: firstly, two di?erent forms of U P Bs in Cm Cnare introduced; secondly,(n- 1)2states UPBs in Cn Cnare constructed;thirdly, another kind of(n-1)2states U P Bs and(n-1)2+1 states U P Bs in Cn Cnare constructed by using graphic analysis; finally, the U P Bs in Cm Cn Csare derived.更多还原