  Entanglement-assisted communication over a random-parameter quantum channel
with either causal or non-causal channel side information (CSI) at the encoder
is considered. This describes a scenario where the quantum channel depends on
the quantum state of the input environment. While Bob, the decoder, has no
access to this state, Alice, the transmitter, performs a sequence of projective
measurements on her environment and encodes her message accordingly. Dupuis
established the entanglement-assisted capacity with non-causal CSI. Here, we
establish characterization in the causal setting, and also give an alternative
proof technique and further observations for the non-causal setting.
