Unbounded violation of tripartite Bell inequalities

We prove that there are tripartite quantum states (constructed from random unitaries) that can lead to arbitrarily large violations of Bell inequalities for dichotomic observables. As a consequence these states can withstand an arbitrary amount of white noise before they admit a description within a local hidden variable model. This is in sharp contrast with the bipartite case, where all violations are bounded by Grothendieck's constant. We will discuss the possibility of determining the Hilbert space dimension from the obtained violation and comment on implications for communication complexity theory. Moreover, we show that the violation obtained from generalized GHZ states is always bounded so that, in contrast to many other contexts, GHZ states do in this case not lead to extremal quantum correlations. The results are based on tools from the theories of operator spaces and tensor norms which we exploit to prove the existence of bounded but not completely bounded trilinear forms from commutative C*-algebras.Comment: Substantial changes in the presentation to make the paper more accessible for a non-specialized reade

Features Extraction of Growth Trend in Social Websites Using Non-linear Genetic Programming

Part 9: Feature ExtractionInternational audienceNonlinear Cartesian Genetic Programming is explored for extraction of features in the growth curve of social web portals and establishment of a prediction model. Daily hit rates of web portals provide the measure of the growth and social establishment behavior over time. Non-linear Cartesian Genetic Programming approach also termed as CGPANN has unique ability of dealing with the nonlinear data as it provides the flexibility in feature selection, network architecture, topology and other necessary parameters selection to establish the desired prediction model. A number of socially established web portals are used to evaluate the performance of the model over a span of two years. Efficient performance is shown by the system keeping the fact in consideration that only single independent web portal data is used for training the network and the same network was used for the other web portals for their performance evaluation. The system performance is significantly good as the system selects only the desired features from the features presented as input and achieves an optimal network and topology that produce the best possible results