Theoretical Study On The Entanglement Of The Heisenberg XYZ Model And Its Application

Quantum information science is a new subject which combines quantum mechanics and information technology. It solves the problems of information processing based on the principle of superposition in quantum mechanics. Quantum information science mainly consists of quantum computation, quantum communication, quantum cryptograph, etc. In recent years, quantum information science has been attracting the interest of a growing community of scientists and technologists because of its potential practical application. As a basic resource of quantum information processing, the entanglement of quantum systems has been studied extensively. An important emerging field is the quantum entanglement in solid state systems such as the Heisenberg chain which is a simple but realistic model for solid-state systems. And it can also be realized in the systems of quantum dots, nuclear spins, cavity QED and optical lattices. So it is necessary to investigate the entanglement of the Heisenberg model. In this thesis, we will focus on studying the entanglement of a two-qubit Heisenberg system.In this thesis, the thermal entanglement of a two-qubit anisotropic Heisenberg XYZ model with both uniform and nonuniform magnetic fields in the x-z plane at thermal equilibrium is investigated. We calculate the concurrence of the two-qubit XYZ spin model, and then study the combined influence of anisotropic parameters, temperature, and both the inhomogeneity and the direction of the magnetic field on the entanglement of the system. Subsequently, we study the combined influences of the anisotropy of the Heisenberg model and the general cases of magnetic fields on the entanglement of a two-qubit anisotropic Heisenberg XYZ model in the presence of quantum decoherence. The results reveal the rule of how the direction of the field and the initial state of the system affect the time evolution of the concurrence in the presence of phase decoherence. Finally, based on the entangled state existed in the two-qubit Heisenberg model, we study the effects of phase decoherence on quantum teleportation process by calculating its fidelity. Our results demonstrates that, for a chosen initial state of the quantum channel, the average fidelity is always larger than 2/3, which shows that such teleportation via the mixed channel is always superior to the classical communication.