  It is known that a reliable geometric quantifier of discord-like correlations
can be built by employing the so-called trace distance. This is used to measure
how far the state under investigation is from the closest "classical-quantum"
one. To date, the explicit calculation of this indicator for two qubits was
accomplished only for states such that the reduced density matrix of the
measured party is maximally mixed, a class that includes Bell-diagonal states.
Here, we first reduce the required optimization for a general two-qubit state
to the minimization of an explicit two-variable function. Using this framework,
we show next that the minimum can be analytically worked out in a number of
relevant cases including quantum-classical and X states. This provides an
explicit and compact expression for the trace distance discord of an arbitrary
state belonging to either of these important classes of density matrices.
