Broadcasting and Teleportation in General Probabilistic Theories

Quantum mechanics is a non-classical probability calculus, but hardly the most general one imaginable: any compact convex set can serve as the ``state space" for a probabilistic model. Using essentially any reasonable notion of a tensor product for such abstract state spaces, many familiar properties of quantum entanglement turn out to be generically non-classical, rather than specifically quantum. In this talk I'll outline proofs of quite generic no-cloning and no-broadcasting theorems -- the latter, substantially simpler than earlier proofs of the quantum-mechanical result. I'll also discuss conditions under which a general probabilistic theory supports a teleportation protocol. Here, the story is rather different, as the existence of such a protocol imposes sharp constraints on both the state spaces and the tensor products involved. (see quant-ph/0611295.)