Long quantum channels for high-quality entanglement transfer

High-quality quantum-state and entanglement transfer can be achieved in an unmodulated spin bus operating in the ballistic regime, which occurs when the endpoint qubits A and B are nonperturbatively coupled to the chain by a suitable exchange interaction j(0). Indeed, the transition amplitude characterizing the transfer quality exhibits a maximum for a finite optimal value j(0)(opt)(N), where N is the channel length. We show that j(0)(opt)(N) scales as N-1/6 for large N and that it ensures a high-quality entanglement transfer even in the limit of arbitrarily long channels, almost independently of the channel initialization. For instance, for any chain length the average quantum-state transmission fidelity exceeds 90% and decreases very little in a broad neighbourhood of j(0)(opt)(N). We emphasize that, taking the reverse point of view, should j(0) be experimentally constrained, high-quality transfer can still be obtained by adjusting the channel length to its optimal value.