  The presence of quantum correlations in a quantum state is related to the
state response to local unitary perturbations. Such response is quantified by
the distance between the unperturbed and perturbed states, minimized with
respect to suitably identified sets of local unitary operations. In order to be
a bona fide measure of quantum correlations, the distance function must be
chosen among those that are contractive under completely positive and trace
preserving maps. The most relevant instances of such physically well behaved
metrics include the trace, the Bures, and the Hellinger distance. To each of
these metrics one can associate the corresponding discord of response, namely
the trace, or Hellinger, or Bures minimum distance from the set of unitarily
perturbed states. All these three discords of response satisfy the basic axioms
for a proper measure of quantum correlations. In the present work we focus in
particular on the Bures distance, which enjoys the unique property of being
both Riemannian and contractive under completely positive and trace preserving
maps, and admits important operational interpretations in terms of state
distinguishability. We compute analytically the Bures discord of response for
two-qubit states with maximally mixed marginals and we compare it with the
corresponding Bures geometric discord, namely the geometric measure of quantum
correlations defined as the Bures distance from the set of classically
correlated quantum states. Finally, we investigate and identify the maximally
quantum correlated two-qubit states according to the Bures discord of response.
These states exhibit a remarkable nonlinear dependence on the global state
purity.
