  We examine the behavior of quantum correlations of spin pairs in a finite
anisotropic $XY$ spin chain immersed in a transverse magnetic field, through
the analysis of the quantum discord and the conventional and quadratic one
way-information deficits. We first provide a brief review of these measures,
showing that the last ones can be obtained as particular cases of a generalized
information deficit based on general entropic forms. All these measures
coincide with an entanglement entropy in the case of pure states, but can be
non-zero in separable mixed states, vanishing just for classically correlated
states. It is then shown that their behavior in the exact ground state of the
chain exhibits similar features, deviating significantly from that of the pair
entanglement below the critical field. In contrast with entanglement, they
reach full range in this region, becoming independent of the pair separation
and coupling range in the immediate vicinity of the factorizing field. It is
also shown, however, that significant differences between the quantum discord
and the information deficits arise in the local minimizing measurement that
defines them. Both analytical and numerical results are provided.
