Abstract
By means of Temperley–Lieb Algebra and topological basis, we make a new realization of topological basis, and get sixteen complete orthonormal topological basis states which are all maximally entangled for four quasi-particles. Then we present an explicit protocol for teleporting an arbitrary two-qubit state via a topological basis entanglement channel. We also show that four bits of classical information can be encoded into a topological basis state by two-particle unitary operations.
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References
Bennett, C.H., Brassard, G., Crepeau, C., Jozsa, R., Peres, A., Wootters, W.K.: Teleporting an unknown quantum state via dual classical. Phys. Rev. Lett. 70, 1895–1899 (1993)
Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)
Chen, P.X., Zhu, S.Y., Guo, G.C.: General form of genuine multipartite entanglement quantum channels for teleportation. Phys. Rev. A 74, 032324 (2006)
Lee, J., Min, H., Oh, S.D.: Multipartite entanglement for entanglement teleportation. Phys. Rev. A 66, 052318 (2002)
Roa, L., Delgado, A., Fuentes-Guridi, I.: Optimal conclusive teleportation of quantum states. Phys. Rev. A 68, 022310 (2003)
Rigolin, G.: Quantum teleportation of an arbitrary two-qubit state and its relation to multipartite entanglement. Phys. Rev. A 71, 032303 (2005)
Yeo, Y., Chua, W.K.: Teleportation and dense coding with genuine multipartite entanglement. Phys. Rev. Lett 96, 060502 (2006)
Dong, H., Xu, D.-Z., Huang, J.-F., Sun, C.-P.: Coherent excitation transfer via the dark-state channel in a bionic system. Light Sci. Appl. 1, e2 (2012). doi:10.1038/lsa.2012.2
Bouwmeester, D., Pan, J.-W., Mattle, K., Eibl, M., Weinfurter, H., Zeilinger, A.: Experimental quantum teleportation. Nature (London) 390, 575–579 (1997)
Pan, J.-W., Daniell, M., Gasparoni, S., Weihs, G., Zeilinger, A.: Experimental demonstration of four-photon entanglement and high-fidelity teleportation. Phys. Rev. Lett. 86, 4435–4438 (2001)
Zhao, Z., Chen, Y.-A., Zhang, A.-N., Yang, T., Briegel, H.J., Pan, J.-W.: Experimental demonstration of five-photon entanglement and open-destination teleportation. Nature (London) 430, 54–58 (2004)
Bennett, C.H., Wiesner, S.J.: ccommunication via one- and two-particle operatiors on Einstein-Podolsky-Rosen states. Phys. Rev. Lett 69, 2881–2884 (1992)
Kitaev, A.: Fault-tolerant quantum computation by anyons. Ann. Phys. (N.Y.) 303, 2 (2003)
Preskill, J.: Quantum Computation, Lecture Notes for Physics, 219 (2004)
Wilczek, F.: Magnetic flux, angular momentum, and statistics. Phys. Rev. Lett 48, 1144–1146 (1982)
Moore, G., Read, N.: Nonabelions in the fractional quantum hall effect. Nucl. Phys. B 360, 362–396 (1991)
Ardonne, E., Schoutens, K.: Schoutens, wavefunctions for topological quantum registers. Ann. Phys. (N.Y.) 322, 201 (2007)
Hikami, K.: Skein theory and topological quantum registers: braiding matrices and topological entanglement entropy of non-Abelian quantum hall states. Ann. Phys. (N.Y.) 323, 1729–1769 (2008)
Feiguin, A., Trebst, S., Ludwig, A.W.W., Troyer, M., Kitaev, A., Wang, Z., Freedman, M.H.: Interacting anyons in topological quantum liquids: the golden chain. Phys. Rev. Lett 98, 160409 (2007)
Nayak, C., Simon, S.H., Stern, A., Freedman, M., Sarma, S.D.: Non-Abelian anyons and topological quantum computation. Rev. Mod. Phys 80, 1083–1159 (2008)
Gils, C., Ardonne, E., Trebst, S., Ludwig, A.W.W., Troyer, M., Wang, Z.: Collective states of interacting anyons, edge states, and the nucleation of topological liquids. Phys. Rev. Lett 103, 070401 (2009)
Hu, S.W., Xue, K., Ge, M.L.: Optical simulation of the Yang-Baxter equation. Phys. Rev. A 78, 022319 (2008)
Wang, G.C., Xue, K., Sun, C.F., Zhou, C.C., Du, G.J.: Quantum Tunneling Effect and Quantum Zeno Effect in a Topological System, e-print arXiv:1012.1474v2
Sun, C.F., Xue, K., Wang, G.C., Zhou, C.C., Du, G.J.: The topological basis realization and the correspongding XXX spin chain. EPL 94, 50001 (2011)
Edwards, C., Arbabi, A., Popescu, G., Goddard, L.L.: Optically monitoring and controlling nanoscale topography during semiconductor etching. Light Sci. Appl. 1, e30 (2012). doi:10.1038/lsa.2012.30
Marx, R., Fahmy, A., Kauffman, L., Lomonaco, S., Spörl, A., Pomplun, N., Schulte-Herbrüggen, T., Myers, J.M., Glaser, S.J.: Nuclear-magnetic-resonance quantum calculations of the Jones polynomial. Phys. Rev. A 81, 032319 (2009)
Temperley, H.N.V., Lieb, E.H.: Relations between the ’Percolation’ and ’Colouring’ problem and other graph-theoretical problems associated with regular planar lattices: some exact results for the ’Percolation’ Problem. Proc. R. Soc. Lond. A 322, 251–280 (1971)
Kauffman, L.H., Lomonacom Jr, S.J.: Braiding operators are universal quantum gates. New J. Phys 6, 134 (2004)
Kauffman, L.: Knots in Physics. World Scientific Publ Co Ltd, Singapore (1991)
Meyer, D.A., Wallach, N.R.: Global entanglement in multiparticle systems. J. Math. Phys. 43, 4273 (2002)
Barnum, H., Knill, E., Ortiz, G., Viola, L.: Generalizations of entanglement based on coherent states and convex sets. Phys. Rev. A 68, 032308 (2003)
Acknowledgments
This work was supported by NSF of China (Grants No. 11175043) and the Fundamental Research Funds for the Central Universities (Grants No. 11QNJJ012)
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Hu, T., Xue, K., Sun, C. et al. Quantum teleportation and dense coding via topological basis. Quantum Inf Process 12, 3369–3381 (2013). https://doi.org/10.1007/s11128-013-0614-9
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DOI: https://doi.org/10.1007/s11128-013-0614-9