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.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.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)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11128-013-0614-9