Relations between entanglement witnesses and Bell inequalities -: art. no. 012321

被引：92

作者：

Hyllus, P ^{[1
]}

Gühne, O

Bruss, D

Lewenstein, M

机构：

[1] Leibniz Univ Hannover, Inst Theoret Phys, D-30167 Hannover, Germany

[2] Austrian Acad Sci, Inst Quantenopt & Quanteninformat, A-6020 Innsbruck, Austria

[3] Univ Dusseldorf, Inst Theoret Phys 3, D-40225 Dusseldorf, Germany

[4] Inst Ciencies Foton, ICFO, Barcelona 08034, Spain

来源：

PHYSICAL REVIEW A | 2005年 / 72卷 / 01期

关键词：

D O I：

10.1103/PhysRevA.72.012321

中图分类号：

O43 [光学];

学科分类号：

070207 ; 0803 ;

摘要：

Bell inequalities, considered within quantum mechanics, can be regarded as nonoptimal witness operators. We discuss the relationship between such Bell witnesses and general entanglement witnesses in detail for the Bell inequality derived by Clauser, Horne, Shimony, and Holt (CHSH) [Phys. Rev. Lett. 23, 880 (1969)]. We derive bounds on how much an optimal witness has to be shifted by adding the identity operator to make it positive on all states admitting a local hidden variable model. In the opposite direction, we obtain tight bounds for the maximal proportion of the identity operator that can be subtracted from such a CHSH witness, while preserving the witness properties. Finally, we investigate the structure of CHSH witnesses directly by relating their diagonalized form to optimal witnesses of two different classes.

引用

页数：7