  A general state of an $m\otimes n$ system is a classical-quantum state if and
only if its associated $A$-correlation matrix (a matrix constructed from the
coherence vector of the party $A$, the correlation matrix of the state, and a
function of the local coherence vector of the subsystem $B$), has rank no
larger than $m-1$. Using the general Schatten $p$-norms, we quantify quantum
correlation by measuring any violation of this condition. The required
minimization can be carried out for the general $p$-norms and any function of
the local coherence vector of the unmeasured subsystem, leading to a class of
computable quantities which can be used to capture the quantumness of
correlations due to the subsystem $A$. We introduce two special members of
these quantifiers; The first one coincides with the tight lower bound on the
geometric measure of discord, so that such lower bound fully captures the
quantum correlation of a bipartite system. Accordingly, a vanishing tight lower
bound on the geometric discord is a necessary and sufficient condition for a
state to be zero-discord. The second quantifier has the property that it is
invariant under a local and reversible operation performed on the unmeasured
subsystem, so that it can be regarded as a computable well-defined measure of
the quantum correlations. The approach presented in this paper provides a way
to circumvent the problem with the geometric discord. We provide some examples
to exemplify this measure.
