Some wiki articles for the things we were talking about:
No-broadcast theorem: http://en.wikipedia.org/wiki/No-broadcast_theorem - “since quantum states cannot be copied in general, they cannot be broadcast.”
No-teleportation theorem: http://en.wikipedia.org/wiki/No_teleportation_theorem - “In quantum information theory, the no-teleportation theorem states that quantum information cannot be measured with complete accuracy.”
No-communication theorem: http://en.wikipedia.org/wiki/No-communication_theorem - “In quantum information theory, a no-communication theorem is a result which gives conditions under which instantaneous transfer of information between two observers is impossible.”
Then, later: “The no-communication theorem thus says shared entanglement alone can not be used to transmit quantum information. Compare this with the no teleportation theorem, which states a classical information channel can not transmit quantum information. (By transmit, we mean transmission with full fidelity.) However, quantum teleportation schemes utilize both resources to achieve what is impossible for either alone.”
Interesting!