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For noncomposite systems in classical and quantum domains, we obtain newinequalities such as the subadditivity and strong subadditivity conditions forShannon entropies and information determined by the probability distributionsand for von Neumann entropies of quantum states determined by the densityoperators. We extend the relations of Shannon and Tsallis entropies to theentropies of conditional probability distributions known for composite systemsto the case of noncomposite systems. We give a review of the approach toconstruct the tomographic-probability distributions for qudit systems andpresent the entropic and information inequalities for spin tomograms, as wellas the subadditivity and strong subadditivity conditions for tomograms of theboth noncomposite and composite system states.

Quantum correlations expressed as information and entropic inequalities for composite and noncomposite systems