搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

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

引用本文:
Citation:

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
PDF
导出引用
  • 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).
    [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

  • [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

  • [1] 白健男, 韩嵩, 陈建弟, 韩海燕, 严冬. 超级里德伯原子间的稳态关联集体激发与量子纠缠. 物理学报, 2023, 72(12): 124202. doi: 10.7498/aps.72.20222030
    [2] 刘腾, 陆鹏飞, 胡碧莹, 吴昊, 劳祺峰, 边纪, 刘泱, 朱峰, 罗乐. 离子阱中以声子为媒介的多体量子纠缠与逻辑门. 物理学报, 2022, 71(8): 080301. doi: 10.7498/aps.71.20220360
    [3] 张金峰, 阿拉帕提·阿不力米提, 杨帆, 艾克拜尔·阿木提江, 唐诗生, 艾合买提·阿不力孜. 不同外加磁场中Kaplan-Shekhtman-Entin-Wohlman-Aharony相互作用对量子失协非马尔科夫演化的影响. 物理学报, 2021, 70(22): 223401. doi: 10.7498/aps.70.20211277
    [4] 杨荣国, 张超霞, 李妮, 张静, 郜江瑞. 级联四波混频系统中纠缠增强的量子操控. 物理学报, 2019, 68(9): 094205. doi: 10.7498/aps.68.20181837
    [5] 李雪琴, 赵云芳, 唐艳妮, 杨卫军. 基于金刚石氮-空位色心自旋系综与超导量子电路混合系统的量子节点纠缠. 物理学报, 2018, 67(7): 070302. doi: 10.7498/aps.67.20172634
    [6] 王灿灿. 量子纠缠与宇宙学弗里德曼方程. 物理学报, 2018, 67(17): 179501. doi: 10.7498/aps.67.20180813
    [7] 程景, 单传家, 刘继兵, 黄燕霞, 刘堂昆. Tavis-Cummings模型中的几何量子失协特性. 物理学报, 2018, 67(11): 110301. doi: 10.7498/aps.67.20172699
    [8] 苏耀恒, 陈爱民, 王洪雷, 相春环. 一维自旋1键交替XXZ链中的量子纠缠和临界指数. 物理学报, 2017, 66(12): 120301. doi: 10.7498/aps.66.120301
    [9] 丛美艳, 杨晶, 黄燕霞. 在不同初态下Dzyaloshinskii-Moriya相互作用及内禀退相干对海森伯系统的量子纠缠的影响. 物理学报, 2016, 65(17): 170301. doi: 10.7498/aps.65.170301
    [10] 王丹琴, 何创创. 双自旋系统中的量子失协问题研究. 物理学报, 2015, 64(4): 043403. doi: 10.7498/aps.64.043403
    [11] 卢道明, 邱昌东. 弱相干场原子-腔-光纤系统中的量子失协. 物理学报, 2014, 63(11): 110303. doi: 10.7498/aps.63.110303
    [12] 李锐奇, 卢道明. 原子与耦合腔相互作用系统中的量子失协. 物理学报, 2014, 63(3): 030301. doi: 10.7498/aps.63.030301
    [13] 杨阳, 王安民. 与Ising链耦合的中心双量子比特系统的量子关联. 物理学报, 2013, 62(13): 130305. doi: 10.7498/aps.62.130305
    [14] 谢美秋, 郭斌. 不同磁场环境下Heisenberg XXZ自旋链中的热量子失协. 物理学报, 2013, 62(11): 110303. doi: 10.7498/aps.62.110303
    [15] 夏建平, 任学藻, 丛红璐, 王旭文, 贺树. 两量子比特与谐振子相耦合系统中的量子纠缠演化特性. 物理学报, 2012, 61(1): 014208. doi: 10.7498/aps.61.014208
    [16] 赵建辉, 王海涛. 应用多尺度纠缠重整化算法研究量子自旋系统的量子相变和基态纠缠. 物理学报, 2012, 61(21): 210502. doi: 10.7498/aps.61.210502
    [17] 刘圣鑫, 李莎莎, 孔祥木. Dzyaloshinskii-Moriya相互作用对量子XY链中热纠缠的影响. 物理学报, 2011, 60(3): 030303. doi: 10.7498/aps.60.030303
    [18] 周南润, 曾宾阳, 王立军, 龚黎华. 基于纠缠的选择自动重传量子同步通信协议. 物理学报, 2010, 59(4): 2193-2199. doi: 10.7498/aps.59.2193
    [19] 胡要花, 方卯发, 廖湘萍, 郑小娟. 二项式光场与级联三能级原子的量子纠缠. 物理学报, 2006, 55(9): 4631-4637. doi: 10.7498/aps.55.4631
    [20] 王成志, 方卯发. 双模压缩真空态与原子相互作用中的量子纠缠和退相干. 物理学报, 2002, 51(9): 1989-1995. doi: 10.7498/aps.51.1989
计量
  • 文章访问数:  5428
  • PDF下载量:  274
  • 被引次数: 0
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

/

返回文章
返回