  Given a quantum channel -- that is, a completely positive trace-preserving
linear map -- as the only communication resource available between two parties,
we consider the problem of characterizing the set of classical noisy channels
that can be obtained from it by means of suitable classical-quantum encodings
and quantum-classical decodings, respectively, on the sender's and the
receiver's side. We consider various classes of linear witnesses and compute
their optimum values in closed form for several classes of quantum channels.
The witnesses that we consider here are formulated as communication games, in
which Alice's aim is to exploit a single use of a given quantum channel to help
Bob guess some information she has received from an external referee.
