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The purpose of these notes is to discuss the relation between the additivityquestions regarding the quantities (Holevo) capacity of a quantum channel T andentanglement of formation of a given bipartite state.  In particular, using the Stinespring dilation theorem, we give a formula forthe channel capacity involving entanglement of formation. This can be used toshow that additivity of the latter for some states can be inferred from theadditivity 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 somewhere a strictly smaller upper bound on the distillable entanglement is known.Group symmetry is used for more sophisticated analysis, giving formulas validfor a class of channels. This is presented in a general framework, extendingrecent findings of Vidal, Dur and Cirac (e-print quant-ph/0112131).  We speculate on a general relation of superadditivity of the entanglement offormation, which would imply both the general additivity of this function undertensor products and of the Holevo capacity (with or without linear costconstraints).Comment: 18 pages LaTeX, 1 eps figure. In v2 some obvious mistakes corrected  and references updated. In v3 slightly more weight on group symmetry. v4  final versio

Remarks on Additivity of the Holevo Channel Capacity and of the Entanglement of Formation