  Clifton, Bub, and Halvorson [Foundations of Physics 33, 1561 (2003)] have
recently argued that quantum theory is characterized by its satisfaction of
three information-theoretic axioms. However, it is not difficult to construct
apparent counterexamples to the CBH characterization theorem. In this paper, we
discuss the limits of the characterization theorem, and we provide some
technical tools for checking whether a theory (specified in terms of the convex
structure of its state space) falls within these limits.
