  We consider the average quantum coherences of typical redits and qudits -
vectors of real and complex Hilbert spaces - with the analytical forms stemming
from the symmetry of Haar-uniformly distributed random pure states. We
subsequently study the response to disorder in spread of the typical quantum
coherence in response to glassy disorder. The disorder is inserted in the state
parameters. Even in the absence of disorder, the quantum coherence
distributions of redits and qudits are not uniform over the range of quantum
coherence, and the spreads are lower for higher dimensions. On insertion of
disorder, the spreads decrease. This decrease in the spread of quantum
coherence distribution in response to disorder is seen to be a generic feature
of typical pure states: we observe the feature for different strengths of
disorder and for various types of disorder distributions, viz. Gaussian,
uniform, and Cauchy-Lorentz. We also find that the quantum coherence
distributions become less asymmetric with increase in dimension and with
infusion of glassy disorder.
