log singularities in studying quantum capacities

Understanding the quantum capacity of a quantum channel is a long standing issue which lies at the center of quantum information theory. Determining the quantum capacity of a general channel or checking that it is positive is difficult. A major source of this difficulty arises due to non-additivity of the one-shot quantum capacity. In this work, we present a new method for checking positivity and non-additivity of the one-shot quantum capacity. This method is based on logarithmic singularities of the von-Neumann entropy. Using this log singularity method, we find a new type of non-additivity where using two very simple channels in parallel, one that doesn't have quantum capacity and a second that has positive one-shot quantum capacity, produces a channel whose one-shot quantum capacity exceeds that of the second channel.