  We present first measure of quantum correlation of an ensemble of multiparty
states. It is based on the idea of minimal entropy production in a locally
distinguishable basis measurement. It is shown to be a relative entropy
distance from a set of ensembles. For bipartite ensembles, which span the whole
bipartite Hilbert space, the measure is bounded below by average relative
entropy of entanglement. We naturally obtain a monotonicity axiom for any
measure of quantum correlation of ensembles. We evaluate this measure for
certain cases. Subsequently we use this measure to propose a complementarity
relation between our measure and the accessible information obtainable about
the ensemble under local operations. The measure along with the monotonicity
axiom are well-defined even for the case of a single system, where the
complementarity relation is seen to be yet another face of the "Heisenberg
uncertainty relation".
