  Recently, the much-used trace distance of coherence was shown to not be a
proper measure of coherence, so a modification of it was proposed. We derive an
explicit formula for this modified trace distance of coherence on pure states.
Our formula shows that, despite satisfying the axioms of proper coherence
measures, it is likely not a good measure to use, since it is maximal (equal to
1) on all except for an exponentially-small (in the dimension of the space)
fraction of pure states.
