  It has recently been pointed out that the geometric quantum discord, as
defined by the Hilbert-Schmidt norm (2-norm), is not a good measure of quantum
correlations, since it may increase under local reversible operations on the
unmeasured subsystem. Here, we revisit the geometric discord by considering
general Schatten p-norms, explicitly showing that the 1-norm is the only p-norm
able to define a consistent quantum correlation measure. In addition, by
restricting the optimization to the tetrahedron of two-qubit Bell-diagonal
states, we provide an analytical expression for the 1-norm geometric discord,
which turns out to be equivalent to the negativity of quantumness. We
illustrate the measure by analyzing its monotonicity properties.
