Qubit portraits of qudit states and quantum correlations

The machinery of qubit portraits of qudit states, recently presented, is considered here in more details in order to characterize the presence of quantum correlations in bipartite qudit states. In the tomographic representation of quantum mechanics, Bell-like inequalities are interpreted as peculiar properties of a family of classical joint probability distributions which describe the quantum state of two qudits. By means of the qubit-portraits machinery a semigroup of stochastic matrices can be associated with a given quantum state. The violation of the CHSH inequalities is discussed in this framework with some examples; we found that quantum correlations in qutrit isotropic states can be detected by the suggested method while it cannot be in the case of qutrit Werner states.