Novel geometrical solution to additivity problem of classical quantum channel capacity

Quantum channel additivity is currently an active area of research in Quantum Information Theory. The additivity conjectures have emerged from an attempt to find a closed form expression for the capacity of a noisy quantum channel. To this day, strict additivity for quantum channel capacity has been conjectured, but not proven. The open questions related to additivity of quantum channel capacities can be discussed by our novel approach. We show an efficient computational geometric method to analyze the additivity property, using quantum Delaunay tessellation on the Bloch ball and quantum relative entropy as distance measure.