  We analyze a task in which classical and quantum messages are simultaneously
communicated via a noisy quantum channel, assisted with a limited amount of
shared entanglement. We derive direct and converse bounds for the one-shot
capacity region, represented by the smooth conditional entropies and the error
tolerance. The proof is based on the randomized partial decoupling theorem,
which is a generalization of the decoupling theorem. The two bounds match in
the asymptotic limit of infinitely many uses of a memoryless channel and
coincide with the previous result obtained by Hsieh and Wilde. Direct and
converse bounds for various communication tasks are obtained as corollaries,
both for the one-shot and asymptotic scenarios.
