Hilbert空间张量积上正算子的SOT-可分离性
发布时间：2018-10-25 14:34
【摘要】：本文给出了无限维的Hilbert空间张量积上一般正算子的可分离性定义,并着重探讨了强算子拓扑(SOT)意义下正算子的可分离性,给出了检测正算子SOT-可分离的充要判据:SOT-不可分离witness判据和SOT-可分离性的正初等算子判据.本文还讨论了不同的SOT-不可分离Witness的比较问题,分别给出它们可以比较、等价、最优、能同时检测某SOT-不可分离正算子以及不能同时检测任何SOT-不可分离正算子的充分必要条件.作为在量子信息理论中的应用,我们构造了一类新的可分离量子态:semi-SSPPT态.同时,极弱拓扑和一致拓扑意义下的正算子的可分离性在本文中也有所涉及,其中,关于SOT可分离性的两个判据对检测WOT-可分离正算子和UWT-可分离正算子的可分离性同样适用,而对于UT-可分离正算子,建立了正偏转置(PPT)判据,并构造了一类UT-可分离的算子:SSPPT算子.
[Abstract]:In this paper, we give the definition of the separability of general positive operators on tensor products of infinite dimensional Hilbert spaces, and discuss emphatically the separability of positive operators in the sense of strong operator topology (SOT). In this paper, the sufficient criteria for SOT- separability of positive operators are given: SOT- inseparability witness criterion and SOT- separable elementary operator criterion. In this paper, we also discuss the comparison problem of different SOT- inseparability Witness, and give their comparison, equivalence, optimum respectively. A sufficient and necessary condition for simultaneous detection of a SOT- inseparable positive operator and for any SOT- inseparable positive operator at the same time. As an application in quantum information theory, we construct a new class of separable quantum states: semi-SSPPT states. At the same time, the separability of positive operators in the sense of very weak topology and uniform topology is also concerned in this paper. Among them, two criteria on SOT separability are also applicable to detect the separability of WOT- separable positive operators and UWT- separable positive operators. For UT- separable positive operators, a positive deflection (PPT) criterion is established, and a class of UT- separable operators, SSPPT operators, are constructed.
【学位授予单位】：太原理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O177.1
本文编号：2293976
[Abstract]:In this paper, we give the definition of the separability of general positive operators on tensor products of infinite dimensional Hilbert spaces, and discuss emphatically the separability of positive operators in the sense of strong operator topology (SOT). In this paper, the sufficient criteria for SOT- separability of positive operators are given: SOT- inseparability witness criterion and SOT- separable elementary operator criterion. In this paper, we also discuss the comparison problem of different SOT- inseparability Witness, and give their comparison, equivalence, optimum respectively. A sufficient and necessary condition for simultaneous detection of a SOT- inseparable positive operator and for any SOT- inseparable positive operator at the same time. As an application in quantum information theory, we construct a new class of separable quantum states: semi-SSPPT states. At the same time, the separability of positive operators in the sense of very weak topology and uniform topology is also concerned in this paper. Among them, two criteria on SOT separability are also applicable to detect the separability of WOT- separable positive operators and UWT- separable positive operators. For UT- separable positive operators, a positive deflection (PPT) criterion is established, and a class of UT- separable operators, SSPPT operators, are constructed.
【学位授予单位】：太原理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O177.1
【相似文献】
相关期刊论文 前10条
1 曹家鼎;用线性弱正算子逼近[J];数学研究与评论;2001年01期
2 张世芳;张长耀;;正算子的若干结果[J];福建师范大学学报(自然科学版);2008年01期
3 张世芳;钟怀杰;;关于正算子的n次方根[J];数学研究;2008年01期
4 谢敦礼;线性正算子序列的点收敛[J];科学通报;1982年22期
5 施容华;;正算子的逆浅议[J];青海师范学院学报(自然科学版);1982年01期
6 侯象乾，薛银川;若干类线性正算子的Λ＿ω（A）类保持性质[J];宁夏大学学报(自然科学版);1995年01期
7 裴君莹,杜鸿科;正算子补问题中的几个性质[J];陕西师范大学学报(自然科学版);1997年01期
8 李海英,杨长森;与正算子有关的几个问题[J];河南师范大学学报(自然科学版);2004年02期
9 谢敦礼;连续正算子序列逼近的阶[J];杭州大学学报(自然科学版);1981年04期
10 罗元;一类线性正算子的整体逼近[J];湖北师范学院学报(自然科学版);1986年02期
相关硕士学位论文 前3条
1 邓春源;巴拿赫格上正算子[D];陕西师范大学;2003年
2 买合木提·买买提;n元τ-可测正算子迹函数的联合凹凸性[D];新疆大学;2011年
3 汪威威;量子混合态密度矩阵的可分性及正算子的方块积[D];陕西师范大学;2007年
，本文编号：2293976
本文链接：https://www.wllwen.com/kejilunwen/yysx/2293976.html
