Lov\'asz's Theta Function, R\'enyi's Divergence and the Sphere-Packing Bound

Lov'asz’s bound to the capacity of a graph and the the sphere-packing bound to the probability of error in channel coding are given a unified presentation as information radii of the Csisz'ar type using the R{'e}nyi divergence in the classical-quantum setting. This brings together two results in coding theory that are usually considered as being of a very different nature, one being a “combinatorial” result and the other being “probabilistic”. In the context of quantum information theory, this difference disappears.