Effect of the Spin-Orbit Interaction (Heisenberg XYZ Model) on Partial Entangled Quantum Network

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DOI: 10.4236/jqis.2014.41001    2,492 Downloads   4,399 Views   Citations


Dzyaloshiniskii-Moriya (DM) interaction in three directions (Dx, Dy and Dz) is used to generate entangled network from partially entangled states in the presence of the spin-orbit coupling. The effect of the spin coupling on the entanglement between any two nodes of the network is investigated. The entanglement is quantified using Woottores concurrence method. It is shown that the entanglement decays as the coupling increases. For larger values of the spin coupling, the entanglement oscillates within finite bounds. For the initially entangled channels, the upper bound does not exceed its initial value, whereas the entanglement reaches its maximum value for the channels generated via indirect interaction.

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Abdel-Aty, A. , Zakaria, N. , Cheong, L. and Metwally, N. (2014) Effect of the Spin-Orbit Interaction (Heisenberg XYZ Model) on Partial Entangled Quantum Network. Journal of Quantum Information Science, 4, 1-17. doi: 10.4236/jqis.2014.41001.


[1] Chuang, I.L. and Nielsen, M.A. (2000) Quantum Computation and Quantum Information. Cambridge University Press, Cambridge.
[2] Prevedel, R., Walther, Ph., Tiefenbacher, F., Böhi, P.L., Kaltenbaek, R., Jennewein, Th. and Zeilinger, A. (2007) High-Speed Linear Optics Quantum Computing Using Active Feed-Forward. Nature, 445, 65-69.
[3] Gottesman, D. and Lo, H.-K. (2003) Proof of Security of Quantum Key Distribution with Two-Way Classical Communications. IEEE Transactions on Information Theory, 49, 457-475.
[4] Perseguers, S., Lapeyre Jr., G.J., Cavalcanti, D., Lewenstein, M. and Acín, A. (2013) Distribution of Entanglement in Large Scale Quantum Networks. Reports on Progress in Physics, 76, Article ID: 096001.
[5] Ahmed, A.-H.M., Cheong, L.Y., Zakaria, N. and Metwally, N. (2013) Dynamics of Information Coded in a Single Cooper Pair Box. International Journal of Theoretical Physics, 52, 1979-1988.
[6] Weberruß, V.A. and Mahler, G. (1998) Quantum Networks. Springer, Berlin.
[7] Briegel, H.-J., Enk, S.J., Cirac, J.I., Zoller, P., Bouwmeeester, D., Pan, J.-W., Daniell, M., Weinfurter, H., Zeilinger, A., Vedral, V., Plenio, M.B. and Knight, P.L. (2000) Quantum Networks and Multi-Particle Entanglement. In: Bouwmeester, D., Ekert, A. and Zeilinger, A., Eds., The Physics of Quantum Information, Springer, Berlin Heidelberg 191-220.
[8] Gao, G. (2013) Cryptanalysis of a Multi-User Quantum Network System and Quantum Communication Using W-Type Entangled States. Journal of the Korean Physical Society, 62, 1093-1096.
[9] Scheidl, Th., Wang, D., Kropatschek, S., Naylor, W., Wittmann, B., Mech, A., Kofler, J., Anisimova, E., Makarov, V., Jennewein, Th., Ursin, R., Zeilinger, A., Ma, X.-S. and Herbst, Th. (2012) Quantum Teleportation and Entanglement Distribution over 100-Kilometre Free-Space Channels. Nature, 489, 269-253.
[10] Laing, L.A. and O’Brien, J. L. (2012) Experimental Realization of Shor’s Quantum Factoring Algorithm Using Qubit Recycling. Nature Photonics, 6, 773-776. http://dx.doi.org/10.1038/nphoton.2012.259
[11] Elliott, Y.C. (2002) Building the Quantum Network. New Journal of Physics, 4, 46-53.
[12] Mink, A., Hershman, B.J., Nakassis, A., Tang, X., Lu, R., Su, D.H., Clark, C.W., Williams, C.J., Hagley, E.W., Wen, J., Bienfang, J. and Gross, A.J. (2004) Quantum Key Distribution with 1.25 gbps Clock Synchronization. Optics Express, 12, 2011-2016. http://dx.doi.org/10.1364/OPEX.12.002011
[13] Buntschu, F., Clausen, B., Felber, N., Gisin, N., Henzen, L., Junod, P., Litzistorf, G., Monbaron, P., Monat, L., Perroud, D., Ribordy, G., Rochas, A., Robyr, S., Tavares, J, Thew, R., Trinkler, P., Ventura, S., Voirol, R., Walenta, N., Stucki, D., Legr, M. and Zbinden, H. (2011) Long-Term Performance of the Swissquantum Quantum Key Distribution Network in a Field Environment. New Journal of Physics, 13, Article ID: 123001.
[14] Ishizuka, H., Klaus, W., Wakui, K., Takeoka, M., Tanaka, A., Yoshino, K., Nambu, Y., Takahashi, S., Tajima, A., Tomita, A., Domeki, T., Hasegawa, T., Sakai, Y., Kobayashi, H., Asai, T., Shimizu, K., Tokura, T., Tsurumaru, T., Matsui, M., Honjo, T., Tamaki, K., Takesue, H., Tokura, Y., Dynes, J.F., Dixon, A.R., Sharpe, A.W., Yuan, Z.L., Shields, A.J., Uchikoga, S., Legre, M., Robyr, S., Trinkler, P., Monat, L., Page, J.-B., Ribordy, G., Poppe, A., Allacher, A., Maurhart, O., Langer, T., Peev, M., Zeilinger, A., Sasaki, M. and Fujiwara, M. (2011) Field Test of Quantum Key Distribution in the Tokyo QKD Network. Optics Express, 19, 10387-10409.
[15] Mtwallay, M. (2011) Entangled Network and Quantum Communications. Physics Letters A, 375, 4268.
[16] Abdel-Aty, A.-H., Cheong, L.Y., Zakaria, N. and Metwally, N. (2013) Quantum Network via Partial Entangled State. The 3rd International Conference on Fundamental and Applied Sciences (ICFAS2014), Universiti Teknologi Petronas, Malaysia, (Accepted) to be appear in AIP Conference Proceedings.
[17] Abdel-Aty, A.-H., Cheong, L.Y., Zakaria, N. and Metwally, N. (2013) Entanglement and Teleportation via Partial Entangled-State Quantum Network. Quantum Information Processing (Submitted).
[18] Darwish, M., Obada, A.-S.F. and El-Barakaty, A. (2011) Purity Loss for a Cooper Pair Box Interacting Dispersively with a Nonclassical Field under Phase Damping. Applied Mathematics & Information Sciences, 5, 122.
[19] Abdel-Khalek, S. and Ahmed, A.M. (2011) Information Entropy of a Superconducting Charge Qubit Interacting with Two Cavity Fields. Applied Mathematics & Information Sciences, 5, 263S-273S.
[20] Moriya, T. (1960) New Mechanism of Anisotropic Superexchange Interaction. Physical Review Letters, 4, 228.
[21] Friesen, M., Chutia, S. and Joynt, R. (2006) Detection and Measurement of the Dzyaloshinskii-Moriya Interaction in Double Quantum Dot Systems. Physical Review B, 73, Article ID: 241304.
[22] Zhang, G.-F. (2007) Thermal Entanglement and Teleportation in a Two Qubit Heisenberg Chain with Dzyaloshinski-Moriya Anisotropic Antisymmetric Interaction. Physical Review A, 75, Article ID: 034304.
[23] Li, S.-S., Ren, T.-Q., Kong, X.-M. and Liu, K. (2012) Thermal Entanglement in the Heisenberg (XXZ) Model with Dzyaloshinskiimoriya Interaction. Physica A, 391, 35-41.
[24] Yeo, Y. (2002) Teleportation via Thermally Entangled States of a Two-Qubit Heisenberg XX Chain. Physical Review A, 66, Article ID: 062312. http://dx.doi.org/10.1103/PhysRevA.66.062312
[25] Ye, M.-Y., Jiang, W., Chen, P.-X., Zhang, Y.-S., Zhou, Z.-W. and Guo, G.-C. (2007) Local Distinguishability of Orthogonal Quantum States and Generators of su(N). Physical Review A, 76, Article ID: 032329.
[26] Li, D.-C. and Cao, Z.-L. (2009) Thermal Entanglement in the Anisotropic Heisenberg (XYZ) Model with Different Inhomogeneous Magnetic Fields. Optics Communications, 282, 1226-1230.
[27] He, Z., Xiong, Z. and Zhang, Y. (2006) Influence of Intrinsic Decoherence on Quantum Teleportation via Two-Qubit Heisenberg (XYZ) Chain. Physics Letters A, 354, 79-83. http://dx.doi.org/10.1016/j.physleta.2006.01.038
[28] Sharma, K.K., Awasthi, S.K. and Pandey, S.N. (2013) Entanglement Sudden Death and Birth in Qubitqutrit Systems under Dzyaloshinskiimoriya Interaction. Quantum Information Processing, 12, 3437-3447.
[29] Rafiee, M., Soltani, M., Mohammadi, H. and Mokhtari, H. (2011) Entanglement Transfer via xxz Heisenberg Chain with dm Interaction. The European Physical Journal D, 63, 473-482.
[30] You, W.L. and Dong, Y.L. (2010) The Entanglement Dynamics of Interacting Qubits Embedded in a Spin Environment with Dzyaloshinsky-Moriya Term. The European Physical Journal D, 57, 439-445.
[31] Obada, A.S.F. and Shaheen, M.E. (2013) Effect of the Thermal Photons on Fischr Information Dynamics for a Dispersive Jeans-Commings Model. Information Sciences Letters, 2, 165-171.
[32] Luo, S.S., Wang, M.M., Chen, X.B. and Yang, Y.X. (2012) Efficient Entanglement Channel Construction Schemes for a Theoretical Quantum Network Model with d Level System. Quantum Information Processing, 11, 1715-1739.
[33] Majumdar, A.S., Adhikari, S., Ghosh, B., Nayak, N. and Roy, S. (2010) Teleportation via Maximally and Non-Maximally Entangled Mixed States. Quantum Information & Computation, 10, 398-419.
[34] Hill, S. and Wootters, W.K. (1997) Entanglement of a Pair of Quantum Bits. Physical Review Letters, 78, 5022-5025.

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