Violating Bell Inequalities Maximally for Two $d$-Dimensional Systems

Details Violating Bell Inequalities Maximally for Two $d$-Dimensional Systems Violating Bell Inequalities Maximally for Two $d$-Dimensional Systems

2005-07-23

arxiv.org/abs/quant-ph/0507227v2

PHYSICAL REVIEW A 74, 032106 (2006)

Physics

Quantum Physics

6 pages, 1 figure. Revised version

Scientific paper

10.1103/PhysRevA.74.032106

We investigate the maximal violation of Bell inequalities for two $d$-dimensional systems by using the method of Bell operator. The maximal violation corresponds to the maximal eigenvalue of the Bell operator matrix. The eigenvectors corresponding to these eigenvalues are described by asymmetric entangled states. We estimate the maximum value of the eigenvalue for large dimension. A family of elegant entangled states $|\Psi>_{\rm app}$ that violate Bell inequality more strongly than the maximally entangled state but are somewhat close to these eigenvectors is presented. These approximate states can potentially be useful for quantum cryptography as well as many other important fields of quantum information.

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