Abstract
In this work, we investigate the multipartite entanglement properties up to four qubits hypergraph states. Our results reveal that the geometric measure seems more efficient than the other measures for measuring the amount of entanglement in these hypergraph states.
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Furusawa, A., Sorensen, J.L., Braunstein, S.L., Fuchs, C.A., Kimble, H.J., Polzik, E.S.: Science 282, 706 (1998)
Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)
Hu, M.L.: Phys. Lett. A 375, 2140 (2011)
Pourkarimi, M.R., Rahnama, M.: Int. J. Theor. Phys. 53, 1415 (2014)
Ekert, A.K.: Phys. Rev. Lett. 67, 661 (1991)
Bennett, C.H., Wiesner, S.J.: Phys. Rev. Lett. 69, 2881 (1992)
Sheng, Y.B., Pan, J., Guo, R., Zhou, L., Wang, L.: ., vol. 58 (2015)
Sheng, Y.B., Zhou, L.: Sci. Rep., vol. 5 (2015)
Zheng, C., Wei, S.: Int. J. Theor. Phys. 57, 2203 (2018)
Haddadi, S., Pourkarimi, M.R., Akhound, A., Ghominejad, M.: Laser phys. Lett., vol. 16 (2019)
Zhou, L., Sheng, Y.B., Long, G.L.: Sci.Bull. 65, 12 (2020)
Chen, S.S., Zhou, L., Zhong, W., Sheng, Y.B., vol. 61 (2018)
Sheng, Y.B., Guo, R., Pan, J., Zhuo, L., Wang, X.F.: Quantum. Inf. Process 14, 963 (2018)
Markham, D., Miyake, A., Virmani, S.: New j. Phys 9, 194 (2007)
Chen, X.Y.: J. Phys. b: at. Mol. Opt. Phys 43, 085507 (2010)
Chen, X.Y.: Front Phys 7, 444 (2012)
Hajdušek, M., Murao, M.: New j. Phys. 15, 013039 (2013)
Guo, Q.Q., Chen, X.Y., Wang, Y.Y.: Chin. Phys. b 23, 050309 (2014)
Chen, X.Y., Wang, L.: J. Phys. a: math. Theor. 47, 415304 (2014)
Gühne, O., Cuquet, M., Steinhoff, F.E.S., Moroder, T., Rossi, M., Bruß, D., Kraus, B., Macchiavello, C.: J. Phys. A: Math. Theor 47, 335303 (2014)
Carvalho, A.R.R., Mintert, F., Buchleitner, A.: Phys. Rev. Lett. 93, 230501 (2004)
Mintert, F., Kus, M., Buchleitner, A.: Phys. Rev. Lett 95, 260502 (2005)
Zhu, X.N., Fei, S.M.: Quantum Inf. Process. 13, 815 (2014)
Zhu, X.N., Li, M., Fei, S.M.: Quantum Inf. Process. 17, 30 (2018)
Love, P.J., Van den Brink, A.M., Smirnov, A. Yu, Amin, M.H.S., Grajcar, M., Ilichev, E., Izmalkov, A., Zagoskin, A.M.: Quantum Inf. Process. 6, 187 (2007)
Hein, M., Eisert, J., Briegel, H.J.: Phys. Rev. A 69, 062311 (2004)
Hein, M., Dür, W., Eisert, J., Raussendorf, R., Van den Nest, M., Briegel, H.J.: .. In: Quantum Computers, Algorithms and Chaos, Edited by Casati, G., Shepelyansky, D.L., Zoller, P., Benenti, G IOS Amsterdam (2006)
Scott, A.J.: Phys. Rev. A 69, 052330 (2004)
Borras, A., Plastino, A.R., Batle, J., Zander, C., Casas, M., Plastino, A.: J. Phys. A Math. Theor. 40, 13407 (2007)
Haddadi, S., Bohloul, M.: Int. J. Theor. Phys. 57, 3912 (2018)
Haddadi, S.: Int. J. Theor. Phys. 56, 2811 (2017)
Akhound, A., Haddadi, S., Chaman Motlagh, M.A.: Mod. Phys. Lett. b33 1950118 (2019)
Haddadi, S., Akhound, A.: Int. J. Theor. Phys. 58, 399 (2019)
Haddadi, S., Pourkarimi, M.R., Akhound, A., Ghominejad, M.: Mod. Phys. Lett. A 34, 1950175 (2019)
Virzì, S., Rebufello, E., Avella, A., Piacentini, F., Gramegna, M., Berchera, I.R., Degiovanni, I.P., Genovese, M.: Sci. Rep. 9, 3030 (2019)
Mansour, M., Daoud, M.: Mod. Phys. Lett. A 34, 1950151 (2019)
Haddadi, S., Akhound, A., Chaman Motlagh, M.A.: Int. J. Theor. Phys. 58, 3406 (2019)
Anders, S., Briegel, H.J.: Phys. Rev. A 73, 022334 (2006)
Severini, S.: Phys. Lett. A 356, 99 (2006)
Riera, C., Jacob, S., Parker, M.G.: Des. Codes cryptogr. 48, 179 (2008)
Cabello, A., Gühne, O., Moreno, P., Rodríguez, D.: Laser Phys. 18, 335 (2008)
Cabello, A., López-Tarrida, A. J., Moreno, P., Portillo, J.R.: Phys. Lett. A 373, 2219 (2009)
Gao, W.B., Yao, X.C., Xu, P., Lu, H., Gühne, O., Cabello, A., Lu, C.Y., Yang, T., Chen, Z.B., Pan, J.W.: Phys. Rev. A 82, 042334 (2010)
Cabello, A., Danielsen, L.E., López-Tarrida, A. J., Portillo, J.R.: Phys. Rev. A 83, 042314 (2011)
Gühne, O., Jungnitsch, B., Moroder, T., Weinstein, Y.S.: Phys. Rev. A 84, 052319 (2011)
Salimi, S., Karami, D., Salimi, E.: Int. J. Theor. Phys. 51, 2031 (2012)
Bell, B.A., Markham, D., Herrera-martí, D.A., Marin, A., Wadsworth, W.J., Rarity, J.G., Tame, M.S.: Nat. Commun. 5, 5480 (2014)
Waegell, M.: Int. J. Quantum inform. 12, 1430005 (2014)
Cui, S.X., Yu, N., Zeng, B.: ., vol. 56 (2015)
Wu, J.Y., Kampermann, H., Bruß, D.: J. Phys. A Math. Theor 49, 055302 (2016)
Dutta, S., Adhikari, B., Banerjee, S., Srikanth, R.: Phys. Rev. A 94, 012306 (2016)
Krenn, M., Gu, X., Zeilinger, A.: Phys. Rev. Lett. 119, 240403 (2017)
Dahlberg, A., Wehner, S.: Phil. Trans. R. Soc. A 376, 20170325 (2018)
Akhound, A., Haddadi, S., Chaman Motlagh, M.A.: J. Rese. Many-body Syst. 8, 1 (2019)
Gu, X., Chen, L., Zeilinger, A., Krenn, M.: Phys. Rev. A 99, 032338 (2019)
Achkir, O., Daoud, M., Mansour, M.: Mod. Phys. Lett. B 31, 1750183 (2017)
Dutta, S., Sarkar, R., Panigrahi, P.K.: Int. J. Theor. Phys. 58, 3927 (2019)
Wei, T.C., Goldbart, P.M.: Phys. Rev. A 68, 042307 (2003)
Wei, T.C., Ericsson, M., Goldbart, P.M., Munro, W.J.: Quantum Inf. Comput. 4, 252 (2004)
Hayashi, M., Markham, D., Murao, M., Owari, M., Virmani, S.: Phys. Rev. Lett. 96, 040501 (2006)
Wei, T.C.: Phys. Rev. A 78, 012327 (2008)
Hajdusek, M., Murao, M.: New J. Phys. 15, 013039 (2013)
Zhang, H.J., Chen, B., Li, M., Fei, S.M., Long, G.L.: Commun. Theor. Phys. 67, 166 (2017)
Gachechiladze, M., Tsimakuridze, N., Gühne, O.: J. Phys. A: math. Theor. 50, 19LT01 (2017)
Tsimakuridze, N., Gühne, O.: J. Phys. A: math. Theor 50, 195302 (2017)
Karimi, N., Heshmati, A., Yahyavi, M., Jafarizadeh, M.A., Mohammadzadeh, A.: Sci. Rep. 9, 14415 (2019)
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We thank Saeed Haddadi for his assistance to provide the computational codes required in this paper.
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Akhound, A., Motlagh, M.A.C. Evaluation of Entanglement Measures for Hypergraph States up to Four Qubits. Int J Theor Phys 59, 2582–2588 (2020). https://doi.org/10.1007/s10773-020-04527-9
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DOI: https://doi.org/10.1007/s10773-020-04527-9