  In this paper we address the issue of universal or robust communication over
quantum channels. Specifically, we consider memoryless communication scenario
with channel uncertainty which is an analog of compound channel in classical
information theory. We determine the quantum capacity of finite compound
channels and arbitrary compound channels with informed decoder. Our approach in
the finite case is based on the observation that perfect channel knowledge at
the decoder does not increase the capacity of finite quantum compound channels.
As a consequence we obtain coding theorem for finite quantum averaged channels,
the simplest class of channels with long-term memory. The extension of these
results to quantum compound channels with uninformed encoder and decoder, and
infinitely many constituents remains an open problem.
