  In this paper, we investigate a high-dimensional quantum state transfer
protocol. An arbitrary unknown high-dimensional state can be transferred with
high fidelity between two remote registers through a XX coupling spin chain of
arbitrary length. The evolution of the state transfer is determined by the
natural dynamics of the chain without external modulation and coupling strength
engineering. As a consequence, entanglement distribution with high efficiency
can be achieved. Also the strong field and high spin quantum number can
counteract partly the effect of finite temperature to ensure high fidelity of
the protocol when the quantum data bus is in the thermal equilibrium state
under an external magnetic field.
