  The purpose of these notes is to discuss the relation between the additivity
questions regarding the quantities (Holevo) capacity of a quantum channel T and
entanglement of formation of a given bipartite state.
  In particular, using the Stinespring dilation theorem, we give a formula for
the channel capacity involving entanglement of formation. This can be used to
show that additivity of the latter for some states can be inferred from the
additivity of capacity for certain channels.
  We demonstrate this connection for a family of group--covariant channels,
allowing us to calculate the entanglement cost for many states, including some
where a strictly smaller upper bound on the distillable entanglement is known.
Group symmetry is used for more sophisticated analysis, giving formulas valid
for a class of channels. This is presented in a general framework, extending
recent findings of Vidal, Dur and Cirac (e-print quant-ph/0112131).
  We speculate on a general relation of superadditivity of the entanglement of
formation, which would imply both the general additivity of this function under
tensor products and of the Holevo capacity (with or without linear cost
constraints).
