Inertia of partial transpose of positive semidefinite matrices

被引：0

作者：

Liang, Yixuan ^{[1
,2
]}

Yan, Jiahao ^{[1
,2
]}

Si, Dongran ^{[1
,2
]}

Chen, Lin ^{[1
,2
,3
]}

机构：

[1] Beihang Univ, LMIB, Beijing 100191, Peoples R China

[2] Beihang Univ, Sch Math Sci, Beijing 100191, Peoples R China

[3] Beihang Univ, Int Res Inst Multidisciplinary Sci, Beijing 100191, Peoples R China

来源：

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL | 2024年 / 57卷 / 12期

关键词：

inertia; positive semidefinite matrix; non-positive-partial-transpose; NPT; ENTANGLEMENT;

D O I：

10.1088/1751-8121/ad3056

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We show that the partial transpose of 9x9 positive semidefinite matrices do not have inertia (4,1,4) and (3,2,4) . It solves an open problem in 'LINEAR AND MULTILINEAR ALGEBRA. Changchun Feng et al, 2022'. We apply our results to construct some inertia, as well as present the list of all possible inertia of partial transpose of 12x12 positive semidefinite matrices.

引用

页数：25

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