Entanglement measure from a minimum distance principle.

Entanglement and quantum correlation are precious resources for quantum technologies implementation based on quantum information science, as, for instance, quantum communication, quantum computing, quantum sensing, and quantum complex systems. Nevertheless, a directly computable measure for the entanglement of multipartite mixed-states is still lacking. In this contribution, we derive from a minimum distance principle an explicit measure able to quantify the degree of quantum correlation for pure or mixed multipartite states. Also, we derive a directly measure of entanglement for the case of a general mixed state. Thus, our measures allow one to distinguish between quantum correlation detached from entanglement and the one induced by entanglement. Since all the relevant quantities in our approach, descend from the geometry structure of the projective Hilbert space, the proposed method is of general application. Finally, we apply the derived measures to some examples of multipartite mixed states.