The Propagation of Quantum Information Through a Spin System

It has been recently suggested that the dynamics of a quantum spin system may provide a natural mechanism for transporting quantum information. We show that one dimensional rings of qubits with fixed (time-independent) interactions, constant around the ring, allow high fidelity communication of quantum states. We show that the problem of maximising the fidelity of the quantum communication is related to a classical problem in fourier wave analysis. By making use of this observation we find that if both communicating parties have access to limited numbers of qubits in the ring (a fraction that vanishes in the limit of large rings) it is possible to make the communication arbitrarily good