Benchmarking quantum channels - the problem of regularization

The classical capacity of a classical channel is found by maximizing the mutual information between the input and output of a single use of the channel. In contrast, the different capacities of quantum channels are obtained by the infinite regularization of particular entropic quantities. In this talk I will review our current understanding of the need for regularization. In particular, I will present some constructions that show that it is not possible to stop the regularization at some finite universal constant independent of the channel and still evaluate the capacity with arbitrary precision.
The talk will be based in arXiv:1408.5115 and arXiv:1502.05326.