  In this paper, we establish an interesting duality between two different
quantum information-processing tasks, namely, classical source coding with
quantum side information, and channel coding over c-q channels. The duality
relates the optimal error exponents of these two tasks, generalizing the
classical results of Ahlswede and Dueck. We establish duality both at the
operational level and at the level of the entropic quantities characterizing
these exponents. For the latter, the duality is given by an exact relation,
whereas for the former, duality manifests itself in the following sense: an
optimal coding strategy for one task can be used to construct an optimal coding
strategy for the other task. Along the way, we derive a bound on the error
exponent for c-q channel coding with constant composition codes which might be
of independent interest.
