  We propose a general measure of non-classical correlations for bipartite
systems based on generalized entropic functions and majorization properties.
Defined as the minimum information loss due to a local measurement, in the case
of pure states it reduces to the generalized entanglement entropy, i.e., the
generalized entropy of the reduced state. However, in the case of mixed states
it can be non-zero in separable states, vanishing just for states diagonal in a
general product basis, like the Quantum Discord. Simple quadratic measures of
quantum correlations arise as a particular case of the present formalism. The
minimum information loss due to a joint local measurement is also discussed.
The evaluation of these measures in a few simple relevant cases is as well
provided, together with comparison with the corresponding entanglement
monotones.
