Study On Teleportation In Heisenberg Thermally Entangled Channels And Entanglement In Quantum Spin System

In this thesis we first study the entanglement in a two-qubit spins in the spin-half Heisenberg XYZ model, and teleport a two-qubit entangled state using this spin chain in the condition of the thermal equilibrium as a quantum channel. We investigate the effectsof the interaction of Z - component J_Z, the inhomogeneous magnetic field b, the anisotropyγand the temperature T on the entanglement and fidelity. In order tocharacterize the quality of the teleported state, we research the average fidelity F_a. Highaverage fidelity of the teleportation and entanglement are obtained when the temperature is very low. Under some condition, we also find that when inhomogeneity is increased to certain value, the average fidelity can exhibit a larger revival than that of less values of b.Secondly, the entanglement in a spin-1 Heisenberg XXZ chain with uniform and nonuniform external magnetic field is investigated. The effects of the external magnetic field, the anisotropy parameter and the temperature on the negativity are discussed respectively. Using the measure of entanglement called 'negativity', we calculate the eigenvalues and eigenvectors of Hamiltonian and the partially transposed density matrix. By theoretical analysis and numerical calculation, we find that the entanglement in this spin chain for any temperature is symmetric with respect to zero magnetic field. In order to show the results clearly, the behavior of negativity is presented for five different cases. In addition, comparing the uniform case with the nonuniform case, we find the negativity can be enhanced with a nonuniform magnetic field under certain condition.