杨-巴克斯特自旋1/2链模型的量子关联研究

摘要

Quantum correlations among different parts of a composite quantum system are the fundamental resource of several applications in quantum information. In general, quantum discord can measure quantum correlations. In that way, the quantum correlations in the Yang-Baxter spin-1/2 chain mode are investigated. In the second part of the paper, the Yang-Baxter spin-1/2 chain modes are constructed from the Yang-Baxter equation. First, we analyze the two matrix representations of Temperly-Lieb algebra. Second, the two solutions of the Yang-Baxter equation are generated using the Yang-Baxterization. Finally, we can change the usual two-particle spin-1/2 chain to the Yang-Baxter spin-1/2 chain modes by means of the unitary Yang-Baxter matrix-R. In the third part, the density matrices of the two chain modes are generated in the thermal equilibrium state in a canonical ensemble. According to the definition of the geometric measure of quantum discord, the analytical expressions of the geometric measure of quantum discord, in the temperature and the external magnetic field, are obtained for the Yang-Baxter spin-1/2 chain modes. When the temperature and the magnetic field intensity increase, the geometric measure of quantum discord decreases. Under the specific conditions, the result of the second chain mode is similar to that of the first one. Then we obtain the numerical results of quantum discord, the geometric measure of quantum discord, and concurrence. It is found that the concurrence can quickly decrease to the value of zero when the temperature is greater than the value of one. At the same time, quantum discord and the geometric measure of quantum discord are not of the value of zero. Thus the quantum discord and the geometric measure of quantum discord can go beyond the concept of entanglement and obtain the“quantumness”of the correlations between the two parts of a system for the Yang–Baxter spin-1/2 chain modes. They are very good quantum resources for quantum information and quantum computing.%量子系统各部分间的量子关联可以作为量子信息应用研究的基础资源。而量子失协是度量量子关联大小的物理量。由此研究杨-巴克斯特自旋1/2链模型的量子关联情况。首先利用两个杨-巴克斯特方程的解得到相应的杨-巴克斯特自旋1/2链模型。然后，计算分析热平衡时杨-巴克斯特自旋1/2链模型的量子失协、几何量子失协和量子纠缠随着温度和外磁场的变化情况。结果表明对于杨-巴克斯特自旋1/2链模型，量子失协和几何量子失协能够比量子纠缠更好地度量量子关联。