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杨-巴克斯特自旋1/2链模型的量子关联研究

苟立丹 王晓茜

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杨-巴克斯特自旋1/2链模型的量子关联研究

苟立丹, 王晓茜

Properties of quantum correlations in the Yang-Baxter spin-1/2 chain mode

Gou Li-Dan, Wang Xiao-Qian
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  • 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.
    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.
    • 基金项目: 国家自然科学基金(批准号: 11305020)资助的课题.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11305020).
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  • [1]

    Olivier H, Zurek W H 2001 Phys. Rev. Lett. 88 017901

    [2]

    Zurek W H 2003 Rev. Mod. Phys. 75 715

    [3]

    Henderson L, Vedral V 2001 J. Phys. A 34 6899

    [4]

    Datta A, Shaji A, Caves C M 2008 Phys. Rev. Lett. 100 050502

    [5]

    Dakic B, Vedral V, Brukner C 2010 Phys. Rev. Lett. 105 190502

    [6]

    Luo S L, Fu S S 2010 Phys. Rev. A 82 034302

    [7]

    Lanyon B P, Barbieri M, Almeida M P, White A G 2008 Phys. Rev. Lett. 101 200501

    [8]

    Dillenschneider R 2008 Phys. Rev. B 78 224413

    [9]

    Sarandy M S 2009 Phys. Rev. A 80 022108

    [10]

    Werlang T, Rigolin G 2010 Phys. Rev. A 81 044101

    [11]

    Chen Y X, Li S W 2010 Phys. Rev. A 81 032120

    [12]

    Lu X M, Ma J, Xi Z J, Wang X G 2011 Phys.Rev.A 83 12327

    [13]

    Maziero J, Werlang T, Fanchini F F, Celeri L C, Serra R M 2010 Phys. Rev. A 81 022116

    [14]

    Shabani A, Lidar D A 2009 Phys. Rev. Lett. 102 100402

    [15]

    Fanchini F F, Werlang T, Brasil C A, Arruda L G E, Caldeira A O 2010 Phys. Rev. A 81 052107

    [16]

    Modi K, Paterek T, Son W, Vedral V, Williamson M 2010 Phys. Rev. Lett. 104 080501

    [17]

    He Z, Li L W 2013 Acta Phys. Sin. 62 180301 (in Chinese) [贺志, 李龙武 2013 物理学报 62 180301]

    [18]

    Yang Y, Wang A M 2013 Acta Phys. Sin. 62 130305 (in Chinese) [杨阳, 王安民 2013 物理学报 62 130305]

    [19]

    Fan K M, Zhang G F 2013 Acta Phys. Sin. 62 130301 (in Chinese) [樊开明, 张国锋 2013 物理学报 62 130301]

    [20]

    Kauffman L H, Lomonaco S J 2004 New J. Phys. 6 134

    [21]

    Yang C N 1967 Phys. Rev. Lett. 19 1312

    [22]

    Baxter R J 1972 Ann. Phys. 70 193

    [23]

    Franko J M, Rowell E C, Wang Z 2006 J. Knot Theory Ramif. 15 413

    [24]

    Zhang Y, Kauffman L H, Ge M L 2005 Int. J. Quant. Inf. 3 669

    [25]

    Zhang Y, Ge M L 2007 Quant. Inf. Process. 3 363

    [26]

    Chen J L, Xue K, Ge M L 2007 Phys. Rev. A 76 042324

    [27]

    Chen J L, Xue K, Ge M L 2008 Ann. Phys. 323 2614

    [28]

    Gou L D, Zhu R H 2012 Chin. Phys. B 21 020305

    [29]

    Gou L D, Wang X Q, Xu Y M, Sun Y Y 2014 Commun. Theor. Phys. 61 349

    [30]

    Liu B, Xue K, Wang G C, Sun C F, Gou L D 2013 Int. J. Quant. Inf. 11 1350018

    [31]

    Temperley H N V, Lieb E H 1971 Proc. Roy. Soc. London. A 322 251

    [32]

    Hu T T, Sun C F, Xue K 2010 Quant. Inf. Process. 9 27

    [33]

    Sun C F, Hu T T, Wang G C, Wu C F, Xue K 2009 Int. J. Quant. Inf. 7 879

    [34]

    Hill S, Wootters W K 1997 Phys.Rev.Lett. 78 5022

    [35]

    Wootters W K 1998 Phys.Rev.Lett. 80 2245

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出版历程
  • 收稿日期:  2014-08-19
  • 修回日期:  2014-11-09
  • 刊出日期:  2015-04-05

杨-巴克斯特自旋1/2链模型的量子关联研究

  • 1. 长春理工大学理学院, 长春 130022
    基金项目: 国家自然科学基金(批准号: 11305020)资助的课题.

摘要: 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.

English Abstract

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