  In this paper we analyze the capacity of a general model for arbitrarily
varying classical-quantum channels (AVCQCs) when the sender and the receiver
use correlation as a resource. In this general model, a jammer has side
information about the channel input. We determine a single letter formula for
the correlation assisted capacity. As an application of our main result, we
determine the correlation assisted common randomness generation capacity. In
this scenario the two channel users have access to correlation as a
resource,and further use an AVCQC with an informed jammer for additional
discussion. The goal is to create common randomness between the two channel
users. We also analyze these capacity formulas when only a small number of
signals from the correlation are available. For the correlation assisted common
randomness generation capacity, we show an additional interesting property: For
a sufficient amount of "public communication", common randomness generation
capacity is Turing computable, however without this public communication
constraint, the correlation assisted common randomness generation capacity is,
in general, not Turing computable. Furthermore, we show that even without
knowing the capacity formula of the deterministic capacity using maximal error
criterion, we can show that it is impossible to evaluate the performance
algorithmically on any current or future digital computer.
