  We propose a characterization and a quantification of general quantum
correlation which is exhibited even by a separable (unentangled) mixed
bipartite state in terms of the nonclassical values of the associated
Kirkwood-Dirac (KD) quasiprobability. Such a general quantum correlation,
wherein entanglement is a subset, is not only intriguing from a fundamental
point of view, but it has also been recognized as a resource in a variety of
schemes of quantum information processing and quantum technology. Given a
bipartite state, we construct a quantity based on the imaginary part the
associated KD quasiprobability defined over a pair of orthonormal product bases
and an optimization procedure over all pairs of such bases. We show that it
satisfies certain requirements expected for a quantifier of general quantum
correlations. It gives a lower bound to the total sum of the quantum standard
deviation of all the elements of the product (local) basis, minimized over all
such bases. It suggests an interpretation as the minimum genuine quantum share
of uncertainty in all possible local von-Neumann projective measurement.
Moreover, it is a faithful witness for entanglement and measurement-induced
nonlocality of pure bipartite states. We then discuss a variational scheme for
its estimation, and based on this, we offer information theoretical meanings of
the general quantum correlation. Our results suggest a deep connection between
the general quantum correlation and the nonclassical values of the KD
quasiprobability and the associated strange weak values.
