Geometric picture of entanglement and Bell inequalities

被引:101
作者
Bertlmann, RA [1 ]
Narnhofer, H [1 ]
Thirring, W [1 ]
机构
[1] Univ Vienna, Inst Theoret Phys, A-1090 Vienna, Austria
来源
PHYSICAL REVIEW A | 2002年 / 66卷 / 03期
关键词
D O I
10.1103/PhysRevA.66.032319
中图分类号
O43 [光学];
学科分类号
070207 ; 0803 ;
摘要
We work in the real Hilbert space H-s of Hermitian Hilbert-Schmidt operators and show that the entanglement witness which shows the maximal violation of a generalized Bell inequality (GBI) is a tangent functional to the convex set Ssubset ofH(s) of separable states. This violation equals the Euclidean distance in H-s of the entangled state to S and thus entanglement, GBI, and tangent functional are only different aspects of the same geometric picture. This is explicitly illustrated in the example of two spins, where also a comparison with familiar Bell inequalities is presented.
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页数:9
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