Bounding the forward classical capacity of bipartite quantum channels

We introduce various measures of forward classical communication for bipartite quantum channels. Since a point-to-point channel is a special case of a bipartite channel, the measures reduce to measures of classical communication for point-to-point channels. As it turns out, these reduced measures have been reported in prior work of Wang et al. on bounding the classical capacity of a quantum channel. As applications, we show that the measures are upper bounds on the forward classical capacity of a bipartite channel. The reduced measures are upper bounds on the classical capacity of a point-to-point quantum channel assisted by a classical feedback channel. Some of the various measures can be computed by semi-definite programming.