There is a small numerical error in the solid ͑black͒ curve of Fig. 5͑b͒. This does not affect any of the results or conclusions quoted in the text. The correct version of the figure is the following: FIG. 5. ͑Color online͒ ͑a͒ shows the maximum fidelity that can be achieved in transferring an input state ͉1͘ to an output state ͉N͘ in a chain of spins coupled by dipole-dipole ͓dashed ͑blue͒ curve͔ or nearest-neighbour ͑solid black curve͒ interactions, as a function of N. The ͑red͒ dotted line at F =2/3 indicates the highest fidelity for classical transmission of a quantum state. We note that the dipole-coupled chain almost always performs better. ͑b͒ shows the time at which the fidelity first peaks in these two systems, plotted on a log 10 scale. The ͑red͒ dotted curve is the function y = L 3 . We see that at large L the dashed ͑blue͒ and dotted ͑red͒ curves are parallel, indicating that the transfer time scales as the cube of the chain length. Units are as specified in Sec. II.
We calculate the fidelity of transmission of a single qubit between distant sites on semi-infinite and finite chains of spins coupled via the magnetic dipole interaction. We show that such systems often perform better than their Heisenberg nearest-neighbour coupled counterparts, and that fidelities closely approaching unity can be attained between the ends of finite chains without any special engineering of the system, although state transfer becomes slow in long chains. We discuss possible optimization methods, and find that, for any length, the best compromise between the quality and the speed of the communication is obtained in a nearly uniform chain of 4 spins.
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