  The use of the so-called entropic inequalities is revisited in the light of
new quantum correlation measures, specially nonlocality. We introduce the
concept of {\it classicality} as the non-violation of these classical
inequalities by quantum states of several multiqubit systems and compare it
with the non-violation of Bell inequalities, that is, {\it locality}. We
explore --numerically and analytically-- the relationship between several other
quantum measures and discover the deep connection existing between them. The
results are surprising due to the fact that these measures are very different
in their nature and application. The cases for $n=2,3,4$ qubits and a
generalization to systems with arbitrary number of qubits are studied here when
discriminated according to their degree of mixture.
