  We consider the compound memoryless quantum multiple-access channel (QMAC)
with two sending terminals. In this model, the transmission is governed by the
memoryless extensions of a completely positive and trace preserving map which
can be any element of a prescribed set of possible maps. We study a
communication scenario, where one of the senders aims for transmission of
classical messages while the other sender sends quantum information. Combining
powerful universal random coding results for classical and quantum information
transmission over point-to-point channels, we establish universal codes for the
mentioned two-sender task. Conversely, we prove that the two-dimensional rate
region achievable with these codes is optimal. In consequence, we obtain a
multi-letter characterization of the capacity region of each compound QMAC for
the considered transmission task.
