  We consider a model of communication via a fully quantum jammer channel with
quantum jammer, quantum sender and quantum receiver, which we dub quantum
arbitrarily varying channel (QAVC). Restricting to finite dimensional user and
jammer systems, we show, using permutation symmetry and a de Finetti reduction,
how the random coding capacity (classical and quantum) of the QAVC is reduced
to the capacity of a naturally associated compound channel, which is obtained
by restricting the jammer to i.i.d. input states.
  Furthermore, we demonstrate that the shared randomness required is at most
logarithmic in the block length, using a random matrix tail bound. This implies
a dichotomy theorem: either the classical capacity of the QAVC is zero, and
then also the quantum capacity is zero, or each capacity equals its random
coding variant.
