Dual- and Multi-rail Encoding

  • Daniel Klaus BurgarthEmail author
  • Vittorio Giovannetti
Part of the Quantum Science and Technology book series (QST)


We review the dual-rail encoding (Burgarth and Bose, Phys Rev A 71:052315, 2005) which demonstrates how the problem of dispersion in quantum state transfer in spin chain communication can be attacked and overcome through performing measurements at the receiver side. We discuss the performance of the dual-rail technique in detail with respect to noise, disorder in the chain couplings (Burgarth and Bose, New J Phys 7:135, 2005) and deviations from a strict one-dimensionality. We then show how the dual-rail method can be made more efficient by using multiple channels (Burgarth et al., Int J Quant Inf 4:405, 2006; J Phys A Math Gen 38:6793, 2005). We provide a convergence theorem which shows that any nearest-neighbor excitation preserving chain is capable of efficient and perfect state transfer using a multi-rail encoding.


Phase Noise Success Probability Spin Chain State Transfer Probability Amplitude 
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  1. 1.
    R. Raussendorf, H.J. Briegel, Phys. Rev. Lett. 86, 5188 (2001)ADSCrossRefGoogle Scholar
  2. 2.
    S. Bose, Phys. Rev. Lett. 91, 207901 (2003)ADSCrossRefGoogle Scholar
  3. 3.
    M. Christandl, N. Datta, T.C. Dorlas, A. Ekert, A. Kay, A.J. Landahl, Phys. Rev. A 71, 032312 (2005)ADSCrossRefGoogle Scholar
  4. 4.
    M.A. Nielsen, I.L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000)zbMATHGoogle Scholar
  5. 5.
    V. Giovannetti, R. Fazio, Phys. Rev. A 71, 032314 (2005)MathSciNetADSCrossRefGoogle Scholar
  6. 6.
    D. Burgarth, S. Bose, Phys. Rev. A 71, 052315 (2005)ADSCrossRefGoogle Scholar
  7. 7.
    D. Burgarth, S. Bose, New. J. Phys. 7, 135 (2005)ADSCrossRefGoogle Scholar
  8. 8.
    D. Burgarth, S. Bose, V. Giovannetti, Int. J. Quant. Inf. 4, 405 (2006)CrossRefzbMATHGoogle Scholar
  9. 9.
    D. Burgarth, V. Giovannetti, S. Bose, J. Phys. A: Math. Gen. 38, 6793 (2005)MathSciNetADSCrossRefzbMATHGoogle Scholar
  10. 10.
    I.L. Chuang, Y. Yamamoto, Phys. Rev. Lett. 76, 4281 (1996)ADSCrossRefGoogle Scholar
  11. 11.
    N. Motoyama, H. Eisaki, S. Uchida, Phys. Rev. Lett. 76, 3212 (1996)ADSCrossRefGoogle Scholar
  12. 12.
    P. Gambardella, A. Dallmeyer, K. Maiti, M.C. Malagoli, W. Eberdardt, K. Kern, C. Carbone, Nature 416, 301 (2002)ADSCrossRefGoogle Scholar
  13. 13.
    T. Yamamoto, Y.A. Pashkin, O. Astafiev, Y. Nakamura, J.S. Tsai, Nature 425, 941 (2003)ADSCrossRefGoogle Scholar
  14. 14.
    A. Romito, R. Fazio, C. Bruder, Phys. Rev. B 71, 100501(R) (2005)Google Scholar
  15. 15.
    C.H. Bennett, D.P. DiVincenzo, J.A. Smolin, Phys. Rev. Lett. 78, 3217 (1997)MathSciNetADSCrossRefzbMATHGoogle Scholar
  16. 16.
    D. Vion, A. Aassime, A. Cottet, P. Joyez, H. Pothier, C. Urbina, D. Esteve, M.H. Devoret, Science 296, 886 (2002)ADSCrossRefGoogle Scholar
  17. 17.
    I. Chiorescu, Y. Nakamura, C.J.P.M. Harmans, J.E. Mooij, Science 299, 1869 (2003)ADSCrossRefGoogle Scholar
  18. 18.
    G.M. Palma, K.A. Suominen, A.K. Ekert, Proc. R. Soc. Lond. A 452, 567 (1996)MathSciNetADSCrossRefzbMATHGoogle Scholar
  19. 19.
    W.Y. Hwang, H. Lee, D.D. Ahn, S.W. Hwang, Phys. Rev. A 62, 062305 (2000)ADSCrossRefGoogle Scholar
  20. 20.
    A. Beige, D. Braun, P. Knight, New J. Phys. 2, 22 (2000)ADSCrossRefGoogle Scholar
  21. 21.
    M. Plenio, P. Knight, Rev. Mod. Phys. 70, 101 (1998)ADSCrossRefGoogle Scholar
  22. 22.
    H.P. Breuer, F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, Oxford, 2002)zbMATHGoogle Scholar
  23. 23.
    G.D. Chiara, D. Rossini, S. Montangero, R. Fazio, Phys. Rev. A 72, 012323 (2005)ADSCrossRefGoogle Scholar
  24. 24.
    L. Dan, Z. Jing-Fu, Chin. Phys. 15, 272 (2006)ADSCrossRefGoogle Scholar
  25. 25.
    P.W. Anderson, Phys. Rev. 109, 1492 (1958)ADSCrossRefGoogle Scholar
  26. 26.
    J.P. Keating, N. Linden, J.C.F. Matthews, A. Winter Phys. Rev. A 75, 012315 (2007)CrossRefGoogle Scholar
  27. 27.
    T.J.G. Apollaro, F. Plastina, Phys. Rev. A 74, 062316 (2006)ADSCrossRefGoogle Scholar
  28. 28.
    D. Burgarth, K. Maruyama, F. Nori, Phys. Rev. A 79, 020305R (2009)Google Scholar
  29. 29.
    B. Sutherland, Phys. Rev. B 12, 3795 (1975)ADSCrossRefGoogle Scholar
  30. 30.
    C. Hadley, A. Serafini, S. Bose, Phys. Rev. A 72, 052333 (2005)ADSCrossRefGoogle Scholar
  31. 31.
    A. Bayat, V. Karimipour, Phys. Rev. A 75, 022321 (2007)ADSCrossRefGoogle Scholar
  32. 32.
    C.H. Bennett, P.W. Shor, IEEE Trans. Inf. Theory 44, 2724 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  33. 33.
    J.R. Schott, Matrix Analysis for Statistics (Wiley-Interscience, Hoboken, 1996)Google Scholar
  34. 34.
    N. Gisin, N. Linden, S. Massar, S. Popescu, Phys. Rev. A 72, 012338 (2005)ADSCrossRefGoogle Scholar
  35. 35.
    A. Kay, M. Ericsson, New. J. Phys. 7, 143 (2005)ADSCrossRefGoogle Scholar
  36. 36.
    B. Vaucher, D. Burgarth, S. Bose, J. Opt. B: Quantum Semiclass. Opt. 7, S356 (2005)ADSCrossRefGoogle Scholar
  37. 37.
    B. Vaucher, Quantum communication of spin-qubits using a collaborative approach. Master’s thesis, Ecole Polytechnique Federale de Lausanne (2005)Google Scholar
  38. 38.
    M. Avellino, A.J. Fisher, S. Bose, Phys. Rev. A 74, 012321 (2006)ADSCrossRefGoogle Scholar
  39. 39.
    A. Kay, Phys. Rev. A 73, 032306 (2006)MathSciNetADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Institute of Mathematics and PhysicsAberystwyth UniversityAberystwythUK
  2. 2.NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNRPisaItaly

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