Local available quantum correlations

Abstract

In this work, local available quantum correlations are studied. They are defined in terms of mutual information of bipartite local measurements done over an optimal local basis complementary to the local basis which defines the respective classical correlations. For two qubits, it is always possible to choose the basis of classical correlations as the set of eigenvectors of $$\sigma _z$$?z (the third Pauli matrix) and complementary bases become the sets of eigenvectors of the observables orthogonal to $$\sigma _z$$?z. It is shown that all states with zero local available quantum correlations are separable but not necessarily strictly classical; this fact puts this kind of correlations in the middle between discord and entanglement. Since in many cases it may suffice to know whether a given state has quantum correlations, the structure of the states with zero local available quantum correlations is presented. It is also shown that there is a close connection between local available quantum correlations and the protocol of entanglement activation developed by Piani et al. (Phys Rev Lett 106:220403, 2011). If a state satisfies the sufficient condition for the entanglement swapping associated with this protocol, this state has nonzero local available quantum correlations.