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.

翻译：经典-量子信道的猜测工作量衡量了在每次只能查询一个状态时，猜测信道传输状态所需付出的代价，该代价在经典预处理的最大化与量子后处理的最小化之间取得平衡。对于任意维度的协变经典-量子信道，我们证明了最优预处理的不变性以及最优后处理的协变性。在量子比特情形下，我们计算了所谓高度对称信息完备经典-量子信道类的最优猜测工作量。