Quantum Teleportation In A Three-qubit Heisenberg Chain

Quantum entanglement, which is viewed as physical resource, plays an important role in quantum computation and quantum communication. For example, quantum teleportation. In the past few years, the bulk of studies have concentrated on a simple solid state system, Heisenberg spin chain. In this thesis, we focus our research in three-qubit Heisenberg models in quantum teleportation.1. We have studied entanglement of a three-qubit ferromagnetic Heisenberg XXZ chain with Dzyaloshinskii-Moriya interaction and obtain the expression for concurrence, which is a function of DM interaction parameter D, the coupling coefficientZJ, external magnetic B and temperature T. It is found that these parameters not only control the entanglement, but also enhance the critical temperatureCT. What’s more, we find the ferromagnetic model has a higher entanglement than antiferromagnetic model.2. We have investigated the thermal entanglement of a three-qubit XXZ Heisenberg model with three-site interactions in an external magnetic field, and the quantum teleportation via this model in thermal equilibrium state. It is found that when the chains are in ground-states both the entanglement and the average fidelity reach their maximal values. The entanglement and the average fidelity become decreased under high temperature, strong magnetic field and small anisotropy parametersZJ. The ferromagnetic system is regarded as the requirement in quantum teleportation. Only XZX+YZY interaction is in favor of entanglement, average fidelity and critical temperatures, while XZY-YZX interaction against all of them.3. We have studied the quantum teleportation via thermally entangled states of three-qubit Heisenberg spin chains with DM interactions under a homogeneous magnetic field carefully. It is found that when the chain is in ground-state the average fidelity reach its maximal values. Both the average fidelity and the critical temperature become larger under a larger coefficientsZJ,smaller parameters J, weaker magnetic field and weaker DM interaction. And the average fidelity decreases with temperature increased. So we can control these parameters to teleport a unknown quantum state successfully. A ferromagnetic chain in this case fits quantum teleportation better.