Search

Article

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

Determing the entanglement of quantum nonbinary graph states

Xu Jian Chen Xiao-Yu Li Hai-Tao

Determing the entanglement of quantum nonbinary graph states

Xu Jian, Chen Xiao-Yu, Li Hai-Tao
PDF
Get Citation
  • Graph states are multipartite entangled states that correspond to mathematical graphs, where the vertices of the graph now play the role of quantum multilevel systems and edges represent interactions of the systems. Graph states are the basis of quantum error correction and one-way quantum computer. We systematically study the entanglement of non-binary graph states. Using iterative algorithm and entanglement bounds, we calculate the entanglement of all the ternary graph states up to nine vertices and parts of quaternary and quinary graph states modulo local unitary transformations and graph isomorphisms. The entanglement measure can be the geometric measure, the measure of relative entropy of entanglement or the measure of logarithmic robustness. We classify the graph states according to the entanglement values obtained. The closest product states obtained in the calculations are studied.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 60972071), the Natural Science Foundation of Zhejiang Province (Grant No. Q12F020072), and the Zhejiang Province Science and Technology Project (Grant No. 2009C31060).
    [1]

    Wei T C, Goldbart P M 2003 Phys. Rev. A 68 042307

    [2]

    Vedral V, Plenio M B, Rippin M A, Knight P L 1997 Phys. Rev. Lett. 78 2275

    [3]

    Vedral V, Plenio M B 1998 Phys. Rev. A 57 1619

    [4]

    Vidal G, Tarrach R 1999 Phys. Rev. A 59 141

    [5]

    Schlingemann D, Werner R F 2002 Phys. Rev. A 65 012308

    [6]

    Cross A, Smith G, Smolin J A, Zeng B 2009 IEEE Trans. Inf. Theory 55 433

    [7]

    Raussendorf R, Briegel H J 2001 Phys. Rev. Lett. 86 5188

    [8]

    Raussendorf R, Browne D E, Briegel H J 2003 Phys. Rev. A 68 022312

    [9]

    Hein M, Eisert J, Briegel H J 2004 Phys. Rev. A 69 062311

    [10]

    Hayashi M, Markham D, Murao M, Owari M, Virmani S 2008 Phys. Rev. A 77 012104

    [11]

    Hayashi M, Markham D, Murao M, Owari M, Virmani S 2006 Phys. Rev. Lett. 96 040501

    [12]

    Markham D, Miyake A, Virmani S 2007 New. J. Phys. 9 194

    [13]

    Jiang L Z, Chen X Y, Ye T Y 2011 Phys. Rev. A 84 042308

    [14]

    Chen X Y 2010 J. Phys. B 43 085507

    [15]

    Hu D, Tang W D, Zhao M S, Chen Q, Yu S Y, Oh C H 2008 Phys. Rev. A 78 012306

    [16]

    Looi S Y, Griffiths R B 2011 Phys. Rev. A 84 052306

    [17]

    Yin J, Qiang Y, Li X Q, Bao X H, Peng C Z, Yang T, Pan G S 2011 Acta Phys. Sin. 60 060308 (in Chinese) [印娟, 钱勇, 李晓强, 包小辉, 彭承志, 杨涛, 潘阁生 2011 物理学报 60 060308]

    [18]

    Yan Z H, Jia X J, Xie C J, Peng K C 2012 Acta Phys. Sin. 61 014206 (in Chinese) [闫智辉, 贾晓军, 谢常德, 彭堃墀 2012 物理学报 61 014206]

  • [1]

    Wei T C, Goldbart P M 2003 Phys. Rev. A 68 042307

    [2]

    Vedral V, Plenio M B, Rippin M A, Knight P L 1997 Phys. Rev. Lett. 78 2275

    [3]

    Vedral V, Plenio M B 1998 Phys. Rev. A 57 1619

    [4]

    Vidal G, Tarrach R 1999 Phys. Rev. A 59 141

    [5]

    Schlingemann D, Werner R F 2002 Phys. Rev. A 65 012308

    [6]

    Cross A, Smith G, Smolin J A, Zeng B 2009 IEEE Trans. Inf. Theory 55 433

    [7]

    Raussendorf R, Briegel H J 2001 Phys. Rev. Lett. 86 5188

    [8]

    Raussendorf R, Browne D E, Briegel H J 2003 Phys. Rev. A 68 022312

    [9]

    Hein M, Eisert J, Briegel H J 2004 Phys. Rev. A 69 062311

    [10]

    Hayashi M, Markham D, Murao M, Owari M, Virmani S 2008 Phys. Rev. A 77 012104

    [11]

    Hayashi M, Markham D, Murao M, Owari M, Virmani S 2006 Phys. Rev. Lett. 96 040501

    [12]

    Markham D, Miyake A, Virmani S 2007 New. J. Phys. 9 194

    [13]

    Jiang L Z, Chen X Y, Ye T Y 2011 Phys. Rev. A 84 042308

    [14]

    Chen X Y 2010 J. Phys. B 43 085507

    [15]

    Hu D, Tang W D, Zhao M S, Chen Q, Yu S Y, Oh C H 2008 Phys. Rev. A 78 012306

    [16]

    Looi S Y, Griffiths R B 2011 Phys. Rev. A 84 052306

    [17]

    Yin J, Qiang Y, Li X Q, Bao X H, Peng C Z, Yang T, Pan G S 2011 Acta Phys. Sin. 60 060308 (in Chinese) [印娟, 钱勇, 李晓强, 包小辉, 彭承志, 杨涛, 潘阁生 2011 物理学报 60 060308]

    [18]

    Yan Z H, Jia X J, Xie C J, Peng K C 2012 Acta Phys. Sin. 61 014206 (in Chinese) [闫智辉, 贾晓军, 谢常德, 彭堃墀 2012 物理学报 61 014206]

  • [1] Liu Min, Huang Yong-Chang. General WGHZ state and its disentanglement and probabilistic teleportation. Acta Physica Sinica, 2005, 54(10): 4517-4523. doi: 10.7498/aps.54.4517
    [2] Chen Peng, Cai You-Xun, Cai Xiao-Fei, Shi Li-Hui, Yu Xu-Tao. Quantum channel establishing rate model of quantum communication network based on entangled states. Acta Physica Sinica, 2015, 64(4): 040301. doi: 10.7498/aps.64.040301
    [3] Liu Shi-You, Zheng Kai-Min, Jia Fang, Hu Li-Yun, Xie Fang-Sen. Entanglement of one- and two-mode combination squeezed thermal states and its application in quantum teleportation. Acta Physica Sinica, 2014, 63(14): 140302. doi: 10.7498/aps.63.140302
    [4] ZHU DONG-PEI, RUAN TU-NAN, SHI MING-JUN, DU JIANG-FENG. THE GEOMETRICAL PICTURE OF MIXED ENTANGLED STATES. Acta Physica Sinica, 2000, 49(10): 1912-1918. doi: 10.7498/aps.49.1912
    [5] Xia Yun-Jie, Gao De-Ying. Entangled coherent states and their nonclassical effects. Acta Physica Sinica, 2007, 56(7): 3703-3708. doi: 10.7498/aps.56.3703
    [6] Lu Hong, She Wei-Long, Tao Meng-Xian. . Acta Physica Sinica, 2002, 51(9): 1996-2001. doi: 10.7498/aps.51.1996
    [7] Liu Hong-Zhan, Ji Yue-Feng. An ameliorated fast phase retrieval iterative algorithm based on the angular spectrum theory. Acta Physica Sinica, 2013, 62(11): 114203. doi: 10.7498/aps.62.114203
    [8] Wang Hai-Xia, Yin Wen, Wang Fang-Wei. Measurement of entanglement in coupled dots. Acta Physica Sinica, 2010, 59(8): 5241-5245. doi: 10.7498/aps.59.5241
    [9] Wang Dong. Direct Bell state measurement for optical beams with correlated amplitude quadratures and anticorrelated phase quadratures. Acta Physica Sinica, 2010, 59(11): 7596-7601. doi: 10.7498/aps.59.7596
    [10] Zhou Nan-Run, Gong Li-Hua, Liu San-Qiu, Zeng Gui-Hua. Quantum communication protocol for data link layer based on entanglement. Acta Physica Sinica, 2007, 56(9): 5066-5070. doi: 10.7498/aps.56.5066
  • Citation:
Metrics
  • Abstract views:  3504
  • PDF Downloads:  385
  • Cited By: 0
Publishing process
  • Received Date:  14 March 2012
  • Accepted Date:  07 June 2012
  • Published Online:  20 November 2012

Determing the entanglement of quantum nonbinary graph states

  • 1. College of Information and Electronic Engineering, Zhejiang Gongshang University, Hangzhou 310018, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant No. 60972071), the Natural Science Foundation of Zhejiang Province (Grant No. Q12F020072), and the Zhejiang Province Science and Technology Project (Grant No. 2009C31060).

Abstract: Graph states are multipartite entangled states that correspond to mathematical graphs, where the vertices of the graph now play the role of quantum multilevel systems and edges represent interactions of the systems. Graph states are the basis of quantum error correction and one-way quantum computer. We systematically study the entanglement of non-binary graph states. Using iterative algorithm and entanglement bounds, we calculate the entanglement of all the ternary graph states up to nine vertices and parts of quaternary and quinary graph states modulo local unitary transformations and graph isomorphisms. The entanglement measure can be the geometric measure, the measure of relative entropy of entanglement or the measure of logarithmic robustness. We classify the graph states according to the entanglement values obtained. The closest product states obtained in the calculations are studied.

Reference (18)

Catalog

    /

    返回文章
    返回