Hidden Correlations and Information-Entropic Inequalities in Systems of Qudits†

We present the results of our study of correlations in noncomposite systems like qudits (N-level atom or spin-j system). We show that they correspond to correlations in composite systems like bipartite or multipartite systems. We establish the correspondence between correlations in noncomposite systems and composite ones using the map of indices labeling the random variables in classical probability theory or matrix elements of density matrices in quantum mechanics. We obtain new information-entropic inequalities for density matrices of noncomposite systems. Also we present Bayes’ formula for noncomposite classical system with one random variable. Finally we discuss the possibility to use hidden correlations and entanglement of a single-qudit state.