Inspired by the notion that the differences between quantum theory and classical physics are best expressed in terms of information theory, Hardy (2001) and Clifton, Bub, and Halvorson (2003) have constructed frameworks general enough to embrace both quantum and classical physics, within which one can invoke principles that distinguish the classical from the quantum. Independently of any view that quantum theory is essentially about quantum information, such frameworks provide a useful tool for exploring the differences between classical and quantum physics, and the relations between the various properties of quantum mechanics that distinguish it from the classical. In particular, we can ask: on which features of quantum physics do our familiar possibility/impossibility theorems depend? It turns out that it is possible to extend the no-cloning theorem and other results, such as the Holevo bound on acquisition of information by a single measurement, beyond the quantum setting.