The thermal entanglement of a three-qubit XXZ Heisenberg model with three-site interactions in an external magnetic field, and the quantum teleportation via this model in thermal equilibrium state are investigated. It is found that entanglement and average fidelity depend on temperature, magnetic field, and anisotropy parameter J Z . Only ferromagnetic system is suitable for quantum teleportation. XZX + YZY interaction is in favor of entanglement, average fidelity, and critical temperatures, while XZY−YZX interaction against all of them. Moreover, we also find entanglement does not fully reflect average fidelity in virtue of study the relation between entanglement and average fidelity.

The quantum teleportation via thermally entangled states of three-qubit Heisenberg spin chains with Dzyaloshinsky-Moriya (DM) interactions under a homogeneous magnetic field has been investigated. It is found that average fidelity and critical temperature depend on not only temperature, magnetic field, but also coupling coefficients, and DM interactions. What is more, we also find that average fidelity has little to do with entanglement.

In this paper, we study carefully the quantum teleportation by means of a channel of a three-qubit Heisenberg XXZ ring, and calculate the fidelity of quantum teleportation. Comparing the four XXZ models: one without three-site interaction, one with XZX +YZY type three-site interaction, one with XZY-YZX type three-site interaction, one with both the two kinds of the three-site interaction, we find some ideal models by which the teleportation only needs a weakest magnetic field and a highest temperature to work successfully. The result could provide a theoretical basis for later experiments.