Quantum Thermal Entanglement And The Entanglement Teleportation In The Heisenberg Model

Seen from the lay of the methodology of scientific research, abundant production often comes from the organic combination of two concepts, while the two concepts look irrelated. A new subject - Quantum Information Theory, which has developed as the combination of information theory and quantum mechanics, is one of the outstanding exemplifications. Quantum information theory has being developed quickly since the 1980s, and it exploits new scopes of the application of quantum mechanics consequently. It provides new principles and new means for the development of information theory in twenty-first century, and has a big advantage over the classical information theory, hence it is able to solve many problems about the information management which classical information theory cannot do. After the development of quantum information theory for more than twenty years, people have achieved a series of significant breakthrough, and quantum information theory has become one of the forefronts of the current international hot topics. In the domain of quantum information theory, as the simplest and most practical solid-state physics system, the Heisenberg model is deemed to one of the most promising physics systems for the realization of quantum communication and quantum computation. The state of a Heisenberg model at thermal equilibrium is a thermal state, and the entanglement in the thermal state is called thermal entanglement. Nowadays, as the important resource for quantum communication and quantum information processing, the thermal entanglement has been extensively applied to various fields such as quantum computation and quantum teleportation.In this dissertation, the quantum thermal entanglement and teleportation of the Heisenberg model are investigated. Main works are as follows:1. The quantum thermal entanglement of two next nearest-neighbor qubits in a four- qubit mixed Heisenberg XX model is calculated and analyzed by concurrence measure of entanglement. The model consists of two kinds of qubits: spin 1/2 and spin S. The results show that the external magnetic field can induce thermal entanglement of two next nearest-neighbor qubits. The amplitude of thermal entanglement is dependent on the spin S. temperature T and homogeneous external magnetic field B. As a result, it is feasible to control thermal entanglement by adjusting the value of external magnetic field B. When S is sufficiently large, we can obtain the high threshold temperature above which there is no thermal entanglement.2. The thermal entanglement and teleportation of a thermally mixed entangled state of two-qubit Heisenberg XXX model under the Dzyaloshinski-Moriya (DM) anisotropic antisymmetric interaction through a noisy quantum channel given by a Werner state is investigated. The results show that a minimum entanglement of the noisy quantum channel must be provided in order to realize entanglement teleportation. It is found that under certain conditions, we can transfer initial state with better fidelity than any classical communication protocol.