Expressions of several information theoretic quantities involve an optimization over auxiliary quantum registers. Entanglement-assisted version of some classical communication problems provides examples of such expressions. Evaluating these expressions requires bounds on the dimension of these auxiliary registers. In the classical case such a bound can usually be obtained based on the
Caratheodory theorem, but we know almost no method to bound the dimension of auxiliary quantum registers. In this talk to compare the classical and quantum sides of the problem the notion of “quantum convexification” will be defined. It will be shown that quantum convexification is strictly richer that the usual classical convexification. Moreover some techniques will be discussed which might be useful for bounding the dimension of quantum auxiliary registers.