  The guesswork of a classical-quantum channel quantifies the cost incurred in
guessing the state transmitted by the channel when only one state can be
queried at a time, maximized over any classical pre-processing and minimized
over any quantum post-processing. For arbitrary-dimensional covariant
classical-quantum channels, we prove the invariance of the optimal
pre-processing and the covariance of the optimal post-processing. In the qubit
case, we compute the optimal guesswork for the class of so-called highly
symmetric informationally complete classical-quantum channels.
