Optimization of Bell operators and visualization of the CGLMP-Bell inequality Export

@article{citeulike:5759066, abstract = {Nonlocality of quantum states is usually verified via the violation of a Bell inequality. Determining if a Bell inequality is preserved or violated for a given state is in general a high-dimensional nonlinear constrained optimization problem. In this work a general numerical optimization approach based on the Euler angle parameterization of SU(N) is proposed. It is not restricted to a certain Bell inequality and can be used for all kinds of qudit systems. As a first application, the method is adapted to the CGLMP-Bell inequality for qutrits and density matrices consisting of mixtures of maximally entangled states. We also utilize this method to improve bounds of a recently proposed multipartite entanglement measure. The comparison of both results explicitly demonstrates that nonlocality detected by the CGLMP-Bell inequality and the amount of entanglement revealed by the measure behave differently, i.e. in general there is no simple relation between Bell inequality violation and the amount of entanglement.}, archivePrefix = {arXiv}, author = {Spengler, Christoph and Huber, Marcus and Hiesmayr, Beatrix C.}, citeulike-article-id = {5759066}, citeulike-linkout-0 = {http://arxiv.org/abs/0907.0998}, citeulike-linkout-1 = {http://arxiv.org/pdf/0907.0998}, day = {6}, eprint = {0907.0998}, keywords = {and, bell, cglmp-bell, inequality, of, operators, optimization, the, visualization}, month = {Jul}, posted-at = {2009-09-09 15:03:25}, priority = {2}, title = {Optimization of Bell operators and visualization of the CGLMP-Bell inequality}, url = {http://arxiv.org/abs/0907.0998}, year = {2009} }

TY - JOUR ID - citeulike:5759066 L3 - citeulike-article-id:5759066 N2 - Nonlocality of quantum states is usually verified via the violation of a Bell inequality. Determining if a Bell inequality is preserved or violated for a given state is in general a high-dimensional nonlinear constrained optimization problem. In this work a general numerical optimization approach based on the Euler angle parameterization of SU(N) is proposed. It is not restricted to a certain Bell inequality and can be used for all kinds of qudit systems. As a first application, the method is adapted to the CGLMP-Bell inequality for qutrits and density matrices consisting of mixtures of maximally entangled states. We also utilize this method to improve bounds of a recently proposed multipartite entanglement measure. The comparison of both results explicitly demonstrates that nonlocality detected by the CGLMP-Bell inequality and the amount of entanglement revealed by the measure behave differently, i.e. in general there is no simple relation between Bell inequality violation and the amount of entanglement. TI - Optimization of Bell operators and visualization of the CGLMP-Bell inequality KW - and KW - bell KW - cglmp-bell KW - inequality KW - of KW - operators KW - optimization KW - the KW - visualization AU - Spengler, Christoph AU - Huber, Marcus AU - Hiesmayr, Beatrix PY - 2009/Jul/06/ UR - http://arxiv.org/abs/0907.0998 ER -