Local unitary operations allow for a unifying approach to the quantification of quantum correlations among the constituents of a bipartite quantum system. For pure states, the distance between a given state and its image under least-perturbing local
unitary operations is a bona fide measure of quantum entanglement, the so-called entanglement of response, which can be extended to mixed states via the convex roof construction. On the other hand, when defined directly on mixed states perturbed by local unitary operations, such a distance turns out to be a bona fide measure of quantum correlations, the so-called discord of response. Exploiting this unified framework, we perform a detailed comparison between two-body entanglement and two-body quantum discord in infinite XY quantum spin chains both in symmetry-preserving and symmetry-breaking ground states as well as in thermal states at finite temperature. The results of the investigation show that in symmetry-preserving ground states the two-point quantum discord dominates over the two-point entanglement, while in symmetrybreaking ground states the two-point quantum discord is strongly suppressed and the two-point entanglement is essentially unchanged. In thermal states, for certain regimes of Hamiltonian parameters, we show that the pairwise quantum discord and the pairwise entanglement can increase with increasing thermal fluctuations.
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 iden
tified 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.
