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General Bell-CHSH type and entropic inequalities based on quantum tomograms
Loran V. Akopyan (Moscow Institute of Physics and Technology), Vladimir I. Man’ko (P.N. Lebedev Physical Institute of the Russian Academy of Sciences, Russian Academy of Sciences)
Abstract: Review of Bell-CHSH type and entropic inequalities in composite quantum correlated systems in the probability representation of states is presented. The upper bounds for some new Bell-CHSH type inequalities within the framework of classical probability theory and in quantum tomography are compared. Violation of Bell-CHSH type inequalities are shown explicitly using the method of averaging in tomographic picture of quantum states. Joint tomographic entropies of multiqubit systems are studied. Limitations on inequalities for tomographic entropies are obtained. A negative result of possible connection between the violation of entropic and Bell-CHSH type inequalities in multi-partite states is reported.