  We examine the quantum correlations of spin pairs in the cyclic $XX$ spin 1/2
chain in a transverse field, through the analysis of the quantum discord, the
geometric discord and the information deficit. It is shown that while these
quantities provide the same qualitative information, being non-zero for all
temperatures and separations and exhibiting the same type of asymptotic
behavior for large temperatures or separations, important differences arise in
the minimizing local measurement that defines them. Whereas the quantum discord
prefers a spin measurement perpendicular to the transverse field, the geometric
discord and information deficit exhibit a perpendicular to parallel transition
as the field increases, which subsists at all temperatures and for all
separations. Moreover, it is shown that such transition signals the change from
a Bell state to an aligned separable state of the dominant eigenstate of the
reduced density matrix of the pair. Full exact results for both the
thermodynamic limit and the finite chain are provided, through the
Jordan-Wigner fermionization.
