Quantum channels have all sorts of capacities: classical, quantum, private, etc. In addition, the capacity typically changes in the presence of additional resources, such as feedback, shared entanglement, etc. Very recently, quite a lot of progress was made regarding the limit of perfect communication in the above settings, at finite block length. I will review some of the most exciting results found, among them the superactivation of zero-error capacities; the fact that entanglement can increase the (0-error) communication capability even of a classical channel; an extension of Lovasz' theta upper bound to entanglement-assisted quantum channels; and a complete characterisation of zero-error channel coding, including a reverse zero-error Shannon theorem, when assisted by general non-signalling correlations.
Based on joint work with T S Cubitt, D Leung, W Matthews, S Severini and R Duan [arXiv:0911.5300, 1002.2514 and 1003.3195]