  If a sender and a receiver lack precise knowledge about the communication
line that connects them, designing a scheme to reliably transmit information
becomes more challenging. This has been studied in classical and quantum
information theory in the context of compound channel models and arbitrarily
varying channel models. However, a fully quantum version of system uncertainty
allows for an even more challenging coding scenario with entangled channel
uses. This type of model has previously been investigated for classical and
quantum capacity. Here, we address the problem of entanglement-assisted
capacity in the presence of such system uncertainty. We find that, under the
assumption of a finite environment dimension, it is equal to a corresponding
compound capacity. Intriguingly, our results imply that in certain fully
quantum arbitrarily varying channel models, the entanglement-assisted capacity
can be positive while the classical capacity is equal to zero, a phenomenon
that does not occur in regular single-channel coding.
