We determine the optimal rates of universal quantum codes for entanglement transmission and generation under channel uncertainty. In the simplest scenario the sender and receiver are provided merely with the information that the channel they use belongs to a given set of channels, so that they are forced to use quantum codes that are reliable for the whole set of channels. This is precisely the quantum analog of the compound channel coding problem. We determine the entanglement transmission and entanglement-generating capacities of compound quantum channels and show that they are equal.

Finally, we show how the results on quantum compound capacities imply those for random quantum capacity of arbitrarily varying quantum channels (AVQC) via Ahlswede's robustification technique.

A final derandomization step leads to a variant of famous Ahlswede dichotomy determining the entanglement transmission capacity of AVQC.

Paper reference: arXiv:0811.4588