The Classical-Quantum Channel with Random State Parameters Known to the Sender

We study an analog of the well-known Gel’fand Pinsker Channel which uses quantum states for the transmission of the data. We consider the case where both the sender’s inputs to the channel and the channel states are to be taken from a finite set (cq-channel with state information at the sender). We distinguish between causal and non-causal channel state information at the sender. The receiver remains ignorant, throughout. We give a single-letter description of the capacity in the first case. In the second case we present two different regularized expressions for the capacity. The direct part of this coding theorem is based on a special class of POVMs which are derived from orthogonal projections onto certain representations of the symmetric groups. This approach supports a reasoning that is inspired by the classical method of types.