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The additivity property of quantum channels is still an open question and an exciting subject of current research. There are some nonunital channels for which strict additivity is known, although the general rule for nonunital quantum channels is still not proven. We analyze the additivity of the amplitude damping channel, which is an important channel in physical implementations and optical communications. The effect of amplitude damping has great importance in optical communications, since this channel model describes energy dissipation. We show an efficient information computational geometric method to analyze the additivity property of the amplitude damping quantum channel, using quantum Delaunay tessellation on the Bloch ball and quantum relative entropy as a distance measure.