Quantum Information Processing

, Volume 10, Issue 1, pp 107–121

Entanglement manipulation via dynamics in multiple quantum spin systems

  • Andrea Casaccino
  • Stefano Mancini
  • Simone Severini
Article

Abstract

We study manipulation of entanglement between two identical networks of quantum mechanical particles. Firstly, we reduce the problem of entanglement transfer to the problem of quantum state transfer. Then, we consider entanglement concentration and purification based on free dynamics on the networks and local measurements on the vertices. By introducing an appropriate measure of efficiency, we characterize the performance of the protocol. We give evidence that such a measure does not depend on the network topology, and we estimate the contribution given by the number of entangled pairs initially shared by the two networks.

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References

  1. 1.
    Kimble H.J.: The quantum internet. Nature 453, 1023–1030 (2008)CrossRefADSPubMedGoogle Scholar
  2. 2.
    Dür W., Briegel H.-J.: Entanglement purification and quantum error correction. Rep. Prog. Phys. 70, 1381–1424 (2007)CrossRefADSGoogle Scholar
  3. 3.
    Horodecki R., Horodecki P., Horodecki M., Horodecki K.: Quantum entanglement. Rev. Mod. Phys. 81(2), 865–942 (2009)CrossRefMathSciNetADSMATHGoogle Scholar
  4. 4.
    Czechlewski,M., Grudka,A., Ishizaka, S.,Wojcik, A.: Entanglement purification protocol for amixture of a pure entangled state and a pure product state. Phys. Rev. A 80, 014303 (pp. 1–6) (2009)Google Scholar
  5. 5.
    Fujii, K., Yamamoto, K.: Entanglement purification with double selection. Phys. Rev. A 80, 042308 (pp. 1–9) (2009)Google Scholar
  6. 6.
    Yang, M., Yan, F., Cao, Z.: Purification of multipartite entanglement by local operations. arXiv:0904.2343Google Scholar
  7. 7.
    Perseguers, S.: Fidelity threshold for long-range entanglement in quantum networks. Phys. Rev. A 81, 012310 (pp. 1–7) (2010)Google Scholar
  8. 8.
    Perseguers, S., Cavalcanti, D., Lapeyre, G.J. Jr., Lewenstein, M., Acin, A.: Multipartite entanglement percolation. Phys. Rev. A 81, 032327 (pp. 1–4) (2010)Google Scholar
  9. 9.
    Perseguers, S., Acin, A., Cirac, J.I., Lewenstein, M.: Quantum complex networks. arXiv: 0907.3283Google Scholar
  10. 10.
    Paunkovic, N., Omar, Y., Bose, S., Vedral, V.: Entanglement concentration using quantum statistics. Phys. Rev. Lett. 88, 187903 (pp. 1–4) (2002)Google Scholar
  11. 11.
    Blume-Kohout, R., Croke, S., Gottesman, D.: Streaming universal distortion-free entanglement concentration. arXiv:0910.5952Google Scholar
  12. 12.
    Maruyama, K., Nori, F.: Entanglement purification without controlled-NOT gates by using the natural dynamics of spin chains. Phys. Rev. A 78, 022312 (pp. 1–5) (2008)Google Scholar
  13. 13.
    Burgath D.: Quantum state transfer and time-dependent disorder in Quantum Chains. Eur. Phys. J. Special Top. 151, 147–156 (2007)CrossRefADSGoogle Scholar
  14. 14.
    Heng F., Korepin V., Roychowdhury V., Hadley C., Bose S.: Quantum communication through spin chain dynamics: an introductory overview. Phys. Rev. B 76, 014428 (2007)CrossRefADSGoogle Scholar
  15. 15.
    Christandl,M., Datta, N., Ekert, A., Landahl, A.: Perfect state transfer in quantum spin networks. Phys. Rev. Lett. 92, 187902 (pp. 1–4) (2004)Google Scholar
  16. 16.
    Christandl,M., Datta, N., Dorlas, T., Ekert, A., Kay, A., Landahl, A.: Perfect transfer of arbitrary states in quantum spin, networks. Phys. Rev. A 71, 032312 (pp. 1–11) (2005)Google Scholar
  17. 17.
    Saxena N., Severini S., Shparlinski I.: Parameters of integral circulant graphs and periodic quantum dynamics. Int. J. Quant. Inf. 5, 417–429 (2007)MATHCrossRefGoogle Scholar
  18. 18.
    Bose S., Casaccino A., Mancini S., Severini S.: Communication in XYZ all-to-all quantum networks with a missing link. Int. J. Quant. Inf 7, 713–723 (2009)MATHCrossRefGoogle Scholar
  19. 19.
    Casaccino A., Lloyd S., Mancini S., Severini S.: Quantum state transfer through a qubit network with energy shift and fluctuations. Int. J. Quant. Inf. 7, 1417–1424 (2009)MATHCrossRefGoogle Scholar
  20. 20.
    Lapeyre, J.,Wehr, J., Lewenstein,M.: Enhancement of entanglement percolation in quantum networks via lattice transformations. Phys. Rev. A 79, 042324 (pp. 1–11) (2009)Google Scholar
  21. 21.
    Acin A., Cirac J.I., Lewenstein M.: Entanglement percolation in quantum networks. Nature Phys. 3, 256–259 (2007)CrossRefADSGoogle Scholar
  22. 22.
    Cuquet, M., Calsamiglia, J.: Entanglement percolation in quantum complex networks. Phys. Rev. Lett. 103, 240503 (pp. 1–4) (2009)Google Scholar
  23. 23.
    Broadfoot, S., Dorner, U., Jaksch, D.: Entanglement percolation with bipartite mixed states. EuroPhys. Lett. 88, 50002 (pp. 1–6) (2009)Google Scholar
  24. 24.
    Werner R.F.: Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model. Phys. Rev. A 40, 4277–4281 (1989)CrossRefADSPubMedGoogle Scholar
  25. 25.
    Wooters W.: Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett. 80, 2245–2248 (1998)CrossRefADSGoogle Scholar
  26. 26.
    Wooters W., Hill S.: Entanglement of a pair of quantum bits. Phys. Rev. Lett. 78, 5022–5025 (1997)CrossRefADSGoogle Scholar
  27. 27.
    Loss D., DiVincenzo D.P.: Quantum computation with quantum dots. Phys. Rev. A 57, 120–126 (1998)CrossRefADSGoogle Scholar
  28. 28.
    Petta J.R., Johnson A.C., Taylor J.M., Laird E.A., Yacoby A., Lukin M.D., Marcus C.M., Hanson M.P., Gossard A.C.: Coherent manipulation of coupled electron spins in semiconductor quantum dots. Science 309, 2180–2191 (2005)CrossRefADSPubMedGoogle Scholar
  29. 29.
    Yu-xi, L.,Wei, L.F., Nori, F.: Preparation of macroscopic quantum superposition states of a cavity field via coupling to a superconducting charge qubit. Phys. Rev. A 71, 063820 (pp. 1–6) (2005)Google Scholar
  30. 30.
    Mandel O., Greiner M., Widera A., Rom T., Hansch T.W., Bloch I.: Controlled collisions for multi-particle entanglement of optically trapped atoms. Nature 425, 937–940 (2003)CrossRefADSPubMedGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Andrea Casaccino
    • 1
    • 2
  • Stefano Mancini
    • 3
    • 4
  • Simone Severini
    • 5
  1. 1.Computer Architecture Group Lab, Information Engineering DepartmentUniversity of SienaSienaItaly
  2. 2.Research Laboratory of ElectronicsMassachusetts Institute of TechnologyCambridgeUSA
  3. 3.School of Science and TechnologyUniversity of CamerinoCamerinoItaly
  4. 4.INFN, Sezione di PerugiaPerugiaItaly
  5. 5.Department of Physics and AstronomyUniversity College LondonLondonUnited Kingdom

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