关于正映射性质的注记
Notes on the Properties of Positive Mappings
禹鸥洋 1任芳国1
作者信息
- 1. 陕西师范大学数学与统计学院,西安 710119
- 折叠
摘要
利用矩阵谱范数及迹范数的性质、矩阵分解、半正定矩阵及分块半正定矩阵的性质和矩阵内积对正映射的性质进行更深入的研究,给出了三个紧凸集端点的特性刻画、获得正映射与其伴随映射的一些性质及完全正映射的一些刻画,这些结果充实了正映射的研究内容并为进一步讨论量子信息问题奠定了潜在的理论基础.
Abstract
By utilizing the properties of matrix spectral norms and trace norms,matrix decomposition,the properties of positive semi-definite matrices and block positive semi-definite matrices,as well as matrix inner product,a more in-depth study is conducted on the properties of positive mappings,the characterization of the endpoints of three compact convex sets,some properties of positive mappings and their adjoint mappings,and some characterizations of completely positive mappings are given,these results enrich the research content of positive mapping and lay a potential theoretical foundation for further discussion of quantum information problems.
关键词
分块矩阵/半正定矩阵/正映射/完全正映射/矩阵分解Key words
block matrix/positive semi-definite matrix/positive mapping/completely positive mapping/matrix decomposition引用本文复制引用
出版年
2024
NETL
NSTL
万方数据