Determining quantum correlations in bipartite systems - from qubit to qutrit and beyond

We advocate the step change in properties of discrete d -level quantum systems, between d = 2 and d ≥ 3. Qubit systems, or multipartite systems containing qubit subsystem, are exceptional in their relative simplicity. One faces a step in complexity in valuating measures of quantum correlations for qutrits and then other higher dimensional qudits. There is a growing number of arguments leading to such conclusion: recently found no-go theorem for generalization of the Peres-Horodecki's PPT criterion [1], change in geometry of state spaces of qubit and higher degree qudits (the so called 'generalized Bloch ball' is not a ball anymore), restricted possibilities for diagonalization of correlation matrices for bipartite systems, more difficult way for handling the set of relevant families of orthogonal projectors.