Separability for Positive Operators on Tensor Product of Hilbert Spaces

作     者：Jin Chuan HOU Jin Fei CHAI Jin Chuan HOU;Jin Fei CHAI

作者机构：College of MathematicsTaiyuan University of TechnologyTaiyuan 030024P.R.China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2021年第37卷第6期

页      面：893-910页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Supported by National Natural Science Foundation of China(Grant No.11171249) 

主　　题：Hilbert spaces tensor products positive operators separability entanglement 

摘      要：The separability and the entanglement(that is,inseparability)of the composite quantum states play important roles in quantum information ***,a quantum state is a trace-class positive operator with trace one acting on a complex separable Hilbert *** this paper,in more general frame,the notion of separability for quantum states is generalized to bounded positive operators acting on tensor product of Hilbert ***,not like the quantum state case,there are different kinds of separability for positive operators with different operator *** types of such separability are discussed;several criteria such as the finite rank entanglement witness criterion,the positive elementary operator criterion and PPT criterion to detect the separability of the positive operators are established;some methods to construct separable positive operators by operator matrices are *** may also make us to understand the separability and entanglement of quantum states better,and may be applied to find new separable quantum states.