Symmetric Hermitian decomposability criterion, decomposition, and its applications

doi:10.1007/s11464-021-0927-4

Front. Math. China

2022, Vol. 17

Issue (5) : 961-986 https://doi.org/10.1007/s11464-021-0927-4

RESEARCH ARTICLE

Symmetric Hermitian decomposability criterion, decomposition, and its applications

Guyan NI(

), Bo YANG

Department of Mathematics, National University of Defense Technology, Changsha 410073, China

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Abstract

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.

Keywords Hermitian tensor tensor decomposition symmetric Hermitian decomposition quantum mixed states quantum entanglement

Corresponding Author(s): Guyan NI

Issue Date: 29 December 2022

Cite this article:

Guyan NI,Bo YANG. Symmetric Hermitian decomposability criterion, decomposition, and its applications[J]. Front. Math. China, 2022, 17(5): 961-986.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-021-0927-4
https://academic.hep.com.cn/fmc/EN/Y2022/V17/I5/961

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