Hidden Quantum Correlations in Single Qudit Systems

We introduce the notion of hidden quantum correlations. We present the mean values of observables depending on one classical random variable described by the probability distribution in the form of correlation functions of two (three, etc.) random variables described by the corresponding joint probability distributions. We develop analogous constructions for the density matrices of quantum states and quantum observables. We consider examples of four-dimensional Hilbert space corresponding to the "quantum roulette" and "quantum compass."