【作者】 张福林；

【导师】 梁麦林；

【作者基本信息】 天津大学 ， 理论物理， 2007， 硕士

【摘要】 量子纠缠是量子信息论的基础,无论是在理论研究中还是在实验测量中都成为令人注目的研究对象。在海森堡模型中自旋粒子间发现的量子热纠缠现象,很有可能得到实际运用。各种不同条件下的海森堡模型中,相邻粒子间的量子热纠缠现象的研究有了很大的进展。本文首先给出量子纠缠及纠缠度的概念,并对量子隐形传态和海森堡模型作相关介绍;而后研究了外界磁场在z方向时,其平均大小和不均匀性对模型纠缠度的影响;着重研究了磁场方向对纠缠的作用,包括均匀磁场和非均匀磁场;本文还讨论了自旋为1的海森堡模型的热纠缠度与外加磁场和耦合常数之间的关系。结果表明,系统的热纠缠受到外界磁场影响是很显著的,并且纠缠度随磁场改变而变化的性质决定于海森堡模型各耦合参数的形式。两个量子位上的磁场平均值和差异值在磁场方向耦合参数改变时表现出对称的关系;保持磁场大小而改变其方向可以控制反铁磁模型热纠缠的大小,可以使不纠缠的铁磁模型产生纠缠,改变纠缠度随磁场大小变化的性质;两个量子位上磁场方向的不同往往可以诱导和增强模型的热纠缠;给自旋为1的XX模型加适当的非均匀磁场可以提高纠缠,z方向耦合参数可以增强纠缠,xy方向的各向异性会降低最大纠缠度而提升强磁场环境中模型的纠缠程度。更多还原

【Abstract】 As the basis of the quantum information, quantum entanglement has been paid much atention both theoretically and experimentally. The thermal entanglement in the Heisenberg model may really have applications in many fields. Many studies have focused on the thermal entanglement between the nearest-neighbor qubit in the Heisenberg model.In this thesis, the introduction about entanglement, quantum teleportation and the Heisenberg model is given firstly. Then, the two-qubit Heisenberg XYZ model under an inhomogeneous z-axis magnetic field is studied. The influence of the direction of magnetic field on entanglement in Heisenberg XXZ model is studied. Both the uniform and nonuniform fields are addressed. The thermal entanglement in a Sin-1 system with two spin coupled by exchange interaction is investigated, both the effects of inhomogeneous magnetic field and couplings being considered.It is found that the influence of magnetic field on the entanglement is in evidence and depends on the couplings. The average and difference values of the magnetic field on two qubits behave symmetry, as the z-component coupling crossing a critical value which depends on the other two couplings. Changing the direction of the filed could control the entanglement of antiferromagnetic model, influence behavior of the entanglement of ferromagnetic model. The difference of the direction of magenetic field on two qubits can induce and inhance the entanglement of Heisenberg model. A suitable inhomogeneous magnetic field may conduce the entanlment of Spin-1 XX model. The entanglement of Spin-1 XXZ model is enhanced by increasing the interaction of z-component . With the increase of the anisotropy in the XY plane, the maximum value of entanglement declines, but the entanglement in a lager magnetic field is improved. Jz更多还原