  We discuss a generalization of the conditional entropy and one-way
information deficit in quantum systems, based on general entropic forms. The
formalism allows to consider simple entropic forms for which a closed
evaluation of the associated optimization problem in qudit-qubit systems is
shown to become feasible, allowing to approximate that of the quantum discord.
As application, we examine quantum correlations of spin pairs in the exact
ground state of finite $XY$ spin chains in a magnetic field through the quantum
discord and information deficit. While these quantities show a similar
behavior, their optimizing measurements exhibit significant differences, which
can be understood and predicted through the previous approximations. The
remarkable behavior of these quantities in the vicinity of transverse and
non-transverse factorizing fields is also discussed.
