  We introduce an infinite family of quantifiers of quantum correlations beyond
entanglement which vanish on both classical-quantum and quantum-classical
states and are in one-to-one correspondence with the metric-adjusted skew
informations. The `quantum $f-$correlations' are defined as the maximum
metric-adjusted $f-$correlations between pairs of local observables with the
same fixed equispaced spectrum. We show that these quantifiers are entanglement
monotones when restricted to pure states of qubit-qudit systems. We also
evaluate the quantum $f-$correlations in closed form for two-qubit systems and
discuss their behaviour under local commutativity preserving channels. We
finally provide a physical interpretation for the quantifier corresponding to
the average of the Wigner-Yanase-Dyson skew informations.
