Research On Quantum Correlation And Quantum Entanglement In Two-qubits Heisenberg Spin Model

The research of quantum entanglement is significant for the development of quantum information theory. By means of quantum entanglement one can achieve some tasks which can not be realized via classical methods, such as quantum teleportation, quantum dense coding and quantum cryptography and so on. In the course of the study of quantum entanglement, Heisenberg spins model which has rich entanglement properties and was extensively studied for last decades, and also lots of literature suggests that spin model as a kind of physical system can realize the quantum computing and quantum communication. It is helpful to explain and discover new physical phenomena to study the entanglement of spin model. With the development of quantum information, entanglement has been found did only one kind of quantum correlation, there exist other non-classical correlation except for quantum entanglement, and the quantum correlation of quantum states includes quantum entanglement and other kinds of non-classical correlation. Moreover, such kinds of non-classical quantum correlation may also play an important role in certain quantum information processes. In Recent years, quantum correlation has attracted much attention of people; we also choose spin model as the research object to do some work in this field, we only discuses the behaviors of quantum correlation and quantum entanglement, however, no analytical expressions of quantum correlation can be obtained by people and further investigation is needed. The main results of this thesis are as follows:1. The quantum correlation of a two-qubit Heisenberg XXZ model has been investigated through applying two independent and controllable magnetic fields (B+b) and (B-b) on the two qubits respectively and changing the coupling parameter Jz, magnetic field B, inhomogeneous magnetic field b and temperature kT. The comparison is made between the behavior of quantum correlation and that of thermal entanglement under one and the same parameters. The results show that quantum correlation can exist for a wider parameter range than thermal entanglement. In addition, for a certain region of parameter, quantum correlation and thermal entanglement exhibit completely different behaviors.2. We investigate the thermal quantum correlation and classical correlation in a two-qubit XY model with Dzyaloshinskii-Moriya (DM) interaction, and also compare with quantum entanglement. We find the behavior of "sudden change" for quantum correlation in this model, and this behavior become more clearly with the increasing of DM interaction, in addition, the quantum correlation equals classical correlation whileΔ= 0 for any DM interaction; the quantum correlation can be enhanced by introducing DM interaction.