For the sake of compactness, we describe entanglement transfer only in the case of spin systems. An ion-trap version of entanglement transfer could easily be accomplished by adding a third ion to the trap. Here, the goal of the control process is to put the system spin in an entangled state […]. As noted above, such states can readily be produced by making the system spin interact directly with the ancilla spin. Suppose, however, that we are not allowed to make the two spins interact directly. It is a well-known fact that if two quantum systems are not entangled initially, they cannot become entangled through the exchange of classical information alone @40#. That is, no classical feedback loop that exchanges information between the system and ancilla can entangle them.
By contrast, because of its ability to transfer quantum information, a quantum feedback loop that mediates between the two spins can readily induce entanglement between them. To accomplish the entanglement transfer, prepare the ancilla spin in the state […], then entangle the ancilla and controller spins by performing a controlled-NOT on the controller spin with the ancilla spin as control. The three spins are now in the state […].
Now perform the quantum feedback procedure given above, supplementing it by applying a third π pulse with frequency […] to flip the controller spin if and only if the system spin is in the state […]. It is easily verified that the final state is […].
That is, the quantum feedback loop accomplishes the goal of producing the desired entanglement between the system spin and the ancilla despite the fact that the system and ancilla spins never interact directly. By contrast, as noted above, a coherent controller that operates by classical feedback cannot drive the system to such an entangled target state without acting on the third spin directly.
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LLOYD, Seth, 2000. Coherent quantum feedback. Physical Review A. 14 July 2000. Vol. 62, no. 2, p. 022108. DOI 10.1103/PhysRevA.62.022108.