  We investigate quantum states that posses both maximum entanglement and
maximum discord between the pertinent parties. Since entanglement (discord) is
defined only for bipartite (two qubit) systems, we shall introduce an
appropriate sum over of all bi-partitions as the associated measure. The
ensuing definition --not new for entanglement-- is thus extended here to
quantum discord. Also, additional dimensions within the parties are considered
({\it qudits}). We also discuss nonlocality (in the form of maximum violation
of a Bell inequality) for all multiqubit systems. The emergence of more
nonlocal states than local ones, all of them possessing maximum entanglement,
will be linked, surprisingly enough, to whether quantum mechanics is defined
over the fields of real or complex numbers.
