Suppose Alice and Bob (arbitrarily named protagonists) are spatially separated. They have at their disposition a classical information channel and share a perfectly entangled bipartite quantum state. Alice has a quantum system in a particular quantum state which she wishes to transfer to Bob. She does not know what the state is. Because measurements disturb quantum information, she cannot just measure her state and send the result to Bob over the channel. She could simply send him the system, but this involves the use of a quantum information channel which she may not have.
However, there is a method which allows her to transfer the state over to Bob by performing a manipulation involving her quantum system and her part of the shared entangled state, then sending 2 classical bits over the classical channel. Once Bob has received the information, he knows how to manipulate his part of the shared state in order to recover the unknown state at his location.
Alice's manipulation destroys her copy of the unknown state (if it did not, it would violate the no-cloning theorem). Note that despite appearances, this scheme could not be used for superluminal communication, because a classical information transfer is an integral part of the procedure.
Details of the manipulations can be found in the following papers:
C.H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. Wootters, "Teleporting an Unknown Quantum State via Dual Classical and Einstein-Podolsky-Rosen Channels", Phys. Rev. Lett. vol. 70, pp 1895-1899 (1993) (the original 6-author research article).
S. Kak, "Teleportation Protocols Requiring Only One Classical Bit", *" class="external">http://arXiv.org/abs/quant-ph/0305085
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