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Transfer of high-dimensional quantum state through an XXZ-Heisenberg quantum spin chain

We propose and analyze an efficient high-dimensional quantum state transfer scheme through an $XXZ$-Heisenberg spin chain in an inhomogeneous magnetic field. By the use of a combination of coherent quantum coupling and free spin-wave approximation, pure unitary evolution results in a perfect high-dimensional swap operation between two remote quantum registers mediated by a uniform quantum data bus, and the feasibility is confirmed by numerical simulations. Also, we observe that either the strong $z$-directional coupling or high quantum spin number can partly suppress the thermal excitations and protect quantum information from the thermal noises when the quantum data bus is in the thermal equilibrium state.