A Quantum Memory Leap

Great question! Let me take some space to elaborate.

The measurement of the first ion does not completely characterize its original quantum state. Before the measurement, it was in a mixture of the nuclear (hyperfine) states, called a superposition. (The quantum state is defined by the relative amounts of the two nuclear states and their relative phase.) The rules of quantum mechanics say that after the measurement finds it, by chance, to be in one of those nuclear states, it stays there. The superposition is destroyed. Thus, there is no way for the researchers to send enough classical information to the other ion to let it be put into the original superposition, because they don't have that information.

However, because of the entanglement, the measurement also changes the second ion, putting it into a particular superposition of its nuclear states, which is closely related to the original quantum state of the first ion. But it is not a teleported version of this original quantum state, yet. It can be turned into a teleported version by a manipulation that I'll describe in a moment. But the exact manipulation that needs to be done is different, depending on which nuclear state the first ion was found in. Thus the complete teleportation requires both the entanglement and the communication of classical information (the results of the first measurement).

What kind of "manipulations" are we talking about? By shining microwaves on the ions, the researchers can controllably change the superposition of nuclear states, without destroying the superposition by measuring it. As it turns out, any combination of two states can be thought of as a point on the surface of a sphere. The north and south poles correspond to the pure states. For a superposition, the latitude and longitude reflect the amount of each pure state and their phase. In this picture, the microwaves cause an overall rotation of the sphere, corresponding to a controlled reallocation between the two pure states.

After the first ion is measured, the second ion is left in one of two superpositions, each of which differs from the original by a 90 degree rotation, but in different directions. The researchers use the result from the first ion to choose the rotation that turns the second ion back into a teleported replica. In addition, they also have to do numerous other controlled rotations during the experiment. In particular, to prove that teleportation was happening, they put the first ion into various superpositions by using rotations of a pure state, and then made repeated measurements on the second ion to show that it received the teleported state.

Although it seems as if something is moving between the distant ions, as far as anyone can tell there is no way to use entanglement or any other aspect of quantum mechanics to transmit information faster than the speed of light.

I hope this helps.

Don Monroe (story author--no relation to the researcher)

Mapou...  Perhaps you just don't understand quantum mechanics very well.   It should be obvious to even the most dimwitted individual... who holds a master's degree in Hyperbolic Topology (m-glee)