  Inspired by the recent work of Bao and Ooguri (BO), we study the
distinguishability of the black hole microstates from the thermal state as
captured by the average of their relative entropies: the Holevo information.
Under the assumption that the vacuum conformal block dominates the entropy
calculation, BO find that the average relative entropy vanishes on spatial
regions less than half the size of the CFT. However, vacuum block dominance
fails for some microstates of the $M=0$ BTZ black hole. We show that this
renders the average relative entropy nonzero even on infinitesimal intervals at
$O(c^0)$.
