Lovász´s theta function, Rényi´s divergence and the sphere-packing bound

Lovász´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 Csiszár type using the Rényi 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.