Discord of response

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.Comment: 10 pages, 2 figures. Improved and expanded version, to be published in J. Phys. A: Math. Ge

The decay of quantum correlations between quantum dot spin qubits and the characteristics of its magnetic field dependence

We address the question of the role of quantum correlations beyond entanglement in context of quantum magnetometry. To this end, we study the evolution of the quantum discord, measured by the rescaled discord, of two electron-spin qubits interacting with an environment of nuclear spins via the hyperfine interaction. We have found that depending on the initial state the evolution can or cannot display indifferentiability points in its time-evolution (due to the energy conservation law), as well as non-trivial dependence on inter-qubit phase. Furthermore, we show that for initial Bell states, quantum correlations display a strong magnetic-field sensitivity which can be utilized for decoherence-driven measurements of the external magnetic field. The potential discord-based measurement is sensitive to a wider range of magnetic field values than the entanglement-based measurement. In principle, entanglement is not a necessary resource for reliable decoherence-driven measurement, while the presence of quantum correlations beyond entanglement is.Comment: 9 pages, 6 figure

Witnessed entanglement and the geometric measure of quantum discord

We establish relations between geometric quantum discord and entanglement quantifiers obtained by means of optimal witness operators. In particular, we prove a relation between negativity and geometric discord in the Hilbert-Schmidt norm, which is slightly different from a previous conjectured one [Phys. Rev. A 84, 052110 (2011)].We also show that, redefining the geometric discord with the trace norm, better bounds can be obtained. We illustrate our results numerically.Comment: 8 pages + 3 figures. Revised version with erratum for PRA 86, 024302 (2012). Simplified proof that discord is bounded by entanglement in any nor

Collapse of the quantum correlation hierarchy links entropic uncertainty to entanglement creation

Quantum correlations have fundamental and technological interest, and hence many measures have been introduced to quantify them. Some hierarchical orderings of these measures have been established, e.g., discord is bigger than entanglement, and we present a class of bipartite states, called premeasurement states, for which several of these hierarchies collapse to a single value. Because premeasurement states are the kind of states produced when a system interacts with a measurement device, the hierarchy collapse implies that the uncertainty of an observable is quantitatively connected to the quantum correlations (entanglement, discord, etc.) produced when that observable is measured. This fascinating connection between uncertainty and quantum correlations leads to a reinterpretation of entropic formulations of the uncertainty principle, so-called entropic uncertainty relations, including ones that allow for quantum memory. These relations can be thought of as lower-bounds on the entanglement created when incompatible observables are measured. Hence, we find that entanglement creation exhibits complementarity, a concept that should encourage exploration into "entanglement complementarity relations".Comment: 19 pages, 2 figures. Added Figure 1 and various remarks to improve clarity of presentatio