  We introduce quantum correlations measures based on the minimal change in
unified entropies induced by local rank-one projective measurements, divided by
a factor that depends on the generalized purity of the system in the case of
non-additive entropies. In this way, we overcome the issue of the artificial
increasing of the value of quantum correlations measures based on non-additive
entropies when an uncorrelated ancilla is appended to the system without
changing the computability of our entropic correlations measures with respect
to the previous ones. Moreover, we recover as limiting cases the quantum
correlations measures based on von Neumann and R\'enyi entropies (i.e.,
additive entropies), for which the adjustment factor becomes trivial. In
addition, we distinguish between total and semiquantum correlations and obtain
some relations between them. Finally, we obtain analytical expressions of the
entropic correlations measures for typical quantum bipartite systems.
