Adversarial guesswork with quantum side information

Abstract: 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.