It appears the Bob and Alice have to use identical systems in order to successfully transmit Bob's state $|\phi\rangle$ to Alice. After transmission (I prefer this term over "teleportation") Alice's state is also $|\phi\rangle$, so I don't see where the question of conservation of energy arises.

What does matter is that in order to "teleport" one qubit between two classical observers, one maximally entangled Bell pair is required. This pair is not entangled any more after the state is transmitted. In order to teleport $X$ qubits, one therefore needs $X$ Bell pairs. Work is done every time a entangled pairs are created from a reservoir of unentangled particles and thus an energy cost is associated with each Bell pair and consequently with each qubit that is teleported.

So there is a consideration of energy but in regards to the cost of the resource which allows the process to occur. But energy is conserved locally at every step of the protocol as @Peter Shor mentioned.

Also see this paper by Masahiro Hotta for some nice ideas on how one can teleport energy between two systems in this manner.

This post imported from StackExchange Physics at 2014-04-01 17:37 (UCT), posted by SE-user user346