Symmetric Hermitian decomposability criterion,decomposition,and its applications  

作　　者：Guyan NI Bo YANG 

机构地区：[1]Department of Mathematics,National University of Defense Technology,Changsha 410073,China

出　　处：《Frontiers of Mathematics in China》2022年第5期961-986,共26页中国高等学校学术文摘·数学（英文）

基　　金：This work was supported by the National Natural Science Foundation of China(Grant No.11871472).

摘　　要：The Hermitian tensor is an extension of Hermitian matrices and plays an important role in quantum information research.It is known that every symmetric tensor has a symmetric CP-decomposition.However,symmetric Hermitian tensor is not the case.In this paper,we obtain a necessary and sufficient condition for symmetric Hermitian decomposability of symmetric Hermitian tensors.When a symmetric Hermitian decomposable tensor space is regarded as a linear space over the real number field,we also obtain its dimension formula and basis.Moreover,if the tensor is symmetric Hermitian decomposable,then the symmetric Hermitian decomposition can be obtained by using the symmetric Hermitian basis.In the application of quantum information,the symmetric Hermitian decomposability condition can be used to determine the symmetry separability of symmetric quantum mixed states.

关 键 词：Hermitian tensor tensor decomposition symmetric Hermitian decomposition quantum mixed states quantum entanglement 

分 类 号：O15[理学—数学]