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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.
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Keywords:
- entanglement /
- nonbinary graph state /
- iterative algorithm
[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]
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[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]
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