NECESSARY CONDITIONS FOR OPTIMALITY OF DECOMPOSABLE ENTANGLEMENT WITNESSES

被引：6

作者：

Kye, Seung-Hyeok ^{[1
,2
]}

机构：

[1] Seoul Natl Univ, Dept Math, Seoul 151742, South Korea

[2] Seoul Natl Univ, Inst Math, Seoul 151742, South Korea

来源：

REPORTS ON MATHEMATICAL PHYSICS | 2012年 / 69卷 / 03期

关键词：

optimal decomposable entanglement witness; product vector; face; positive map; POSITIVE LINEAR-MAPS; MATRIX ALGEBRAS; FACIAL STRUCTURES; SEPARABILITY; STATES;

D O I：

10.1016/S0034-4877(13)60007-5

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

It is well known that the support of an optimal decomposable entanglement witness is completely entangled. We add two more necessary conditions for the optimality: The orthogonal complement of the support must have a nonzero product vector; another one will be given in terms of related faces of a convex cone. With these necessary conditions, we show that there exist examples of nonoptimal decomposable entanglement witnesses which are the partial transposes of positive semi-definite matrices supported on completely entangled spaces, whenever both of the local dimensions are greater than or equal to three.

引用

页码：419 / 426

页数：8

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