Communication over Quantum Channels with Parameter Estimation

Communication over a random-parameter quantum channel when the decoder reconstructs the parameter sequence is considered in different scenarios. Regularized formulas are derived for the capacity-distortion regions with strictly-causal, causal, or non-causal channel side information (CSI) available at the encoder, and also without CSI. Single-letter characterizations are established in special cases. In particular, a single-letter formula is given for entanglement-breaking channels when CSI is not available. As a consequence, we obtain regularized formulas for the capacity of random-parameter quantum channels with CSI, generalizing previous results on classical-quantum channels.