  In this work we prove that the possibility of superactivation of quantum
channel capacities is determined by the mathematical properties of the quantum
relative entropy function. Before our work this fundamental and purely
mathematical connection between the quantum relative entropy function and the
superactivation effect was completely unrevealed. We demonstrate the results
for the quantum capacity; however the proposed theorems and connections hold
for all other channel capacities of quantum channels for which the
superactivation is possible.
