  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."
