Effect of spin-orbit interaction on entanglement of two-qubit Heisenberg XYZ systems in an inhomogeneous magnetic field

The role of spin-orbit interaction in the ground state and thermal entanglement of a Heisenberg XYZ two-qubit system in the presence of an inhomogeneous magnetic field is investigated. We show that the ground state entanglement tends to vanish suddenly for a certain value of the spin-orbit parameter D and, when D crosses its critical value D-c, the entanglement undergoes a revival. Indeed, when D crosses its critical value (D-c), the ground state entanglement tends to its maximum value (C=1). Also, at finite temperatures there are revival regions in the D-T plane. In these regions, entanglement first increases with increasing temperature and then decreases and ultimately vanishes for temperatures above a critical value. We find that this critical temperature is an increasing function of D and that the amount of entanglement in the revival region depends on the spin-orbit parameter. Therefore when spin-orbit interaction is included larger thermal entanglement can exist at higher temperatures. We also show that the rate of enhancement of thermal entanglement by D is not the same for ferromagnetic (J(z)< 0) and antiferromagnatic (J(z)>0) chains. The entanglement teleportation via the quantum channel constructed by the above system is also investigated, and the influence of the spin-orbit interaction on the fidelity of teleportation and entanglement of replica states is studied. We show that, by introducing spin-orbit interaction, the entanglement of the replica state and fidelity of teleportation can be increased for the case of J(z)< 0. We also argue that a minimal entanglement of the channel is required to realize efficient entanglement teleportation and, in the case of J(z)< 0, this minimal entanglement can be achieved by introducing spin-orbit interaction.