Channel capacities via $p$-summing norms

Understand

In this paper we show how \emph{the metric theory of tensor products} developed by Grothendieck perfectly fits in the study of channel capacities, a central topic in \emph{Shannon's information theory}.

• Furthermore, in the last years Shannon's theory has been generalized to the quantum setting to let the \emph{quantum information theory} step in.
• In this paper we consider the classical capacity of quantum channels with restricted assisted entanglement.
• In particular these capacities include the classical capacity and the unlimited entanglement-assisted classical capacity of a quantum channel.