Quantum State Transfer with Limited Resources

  • Carlo Di FrancoEmail author
  • Mauro Paternostro
  • M. S. Kim
Part of the Quantum Science and Technology book series (QST)


In the quest for the achievement of realistic quantum state transfer protocols, relaxing the required conditions is a fundamental step. The use of multi-particle systems for the purpose of quantum information processing is made hard by a number of technical difficulties, related in particular to the lack of addressability of their single elements. We have thus to research novel ways to bypass these problems. Even if investigating the whole evolution of a quantum system is surely interesting, considering the behaviour of a few characteristic features could help us to find striking strategies in the context outlined above. This is exactly the idea at the basis of the method presented in this chapter, which we name information flux approach. Through it, we can design protocols for quantum state transfer in limited-control scenarios. In particular, we focus our interest in finding a way to avoid the initialisation of the spin chain. Different cases are described throughout the chapter.


Entangle State Spin Chain State Transfer Quantum Information Processing Recurrence Formula 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



CDF and MP’s work was supported by the UK EPSRC with a grant under the “New Directions for EPSRC Research Leaders” initiative (EP/G004759/1). MSK’s work was supported by the grant NPRP 4-554-1-094 from Qatar National Research Fund. MP thanks the UK EPSRC for a Career Acceleration Fellowship.


  1. 1.
    C. Di Franco, M. Paternostro, G. M. Palma, M. S. Kim, Phys. Rev. A 76, 042316 (2007); C. Di Franco, M. Paternostro, G. M. Palma, Int. J. Quant. Inf. 6(Supp. 1), 659 (2008)Google Scholar
  2. 2.
    S. Bose, Contemp. Phys. 48, 13 (2007)ADSCrossRefGoogle Scholar
  3. 3.
    M. Christandl, N. Datta, A. Ekert, A. J. Landahl, Phys. Rev. Lett. 92, 187902 (2004); C. Albanese, M. Christandl, N. Datta, A. Ekert, Phys. Rev. Lett. 93, 230502 (2004); G. M. Nikolopoulos, D. Petrosyan, P. Lambropoulos, Europhys. Lett. 65, 297 (2004); G. M. Nikolopoulos, D. Petrosyan, P. Lambropoulos, J. Phys.: Condens. Matter 16, 4991 (2004); M. Christandl, N. Datta, T. C. Dorlas, A. Ekert, A. Kay, A. J. Landahl, Phys. Rev. A 71, 032312 (2005)Google Scholar
  4. 4.
    S. Bose, Phys. Rev. Lett. 91, 207901 (2003)ADSCrossRefGoogle Scholar
  5. 5.
    S. Sachdev, Quantum Phase Transitions (Cambridge University Press, Cambridge, 1999); E. Lieb, T. Schultz, D. Mattis, Ann. Phys. 16, 407 (1961)Google Scholar
  6. 6.
    C. Di Franco, M. Paternostro, D. I. Tsomokos, S. F. Huelga, Phys. Rev. A 77, 062337 (2008)ADSCrossRefGoogle Scholar
  7. 7.
    Y. Makhlin, G. Schön, A. Schnirman, Rev. Mod. Phys. 73, 357 (2001); D. Vion, A. Aassime, A. Cottet, P. Joyez, H. Pothier, C. Urbina, D. Esteve, M. H. Devoret, Science 296, 886 (2002); D. I. Tsomokos, M. J. Hartmann, S. F. Huelga, M. B. Plenio, New J. Phys. 9, 79 (2007)Google Scholar
  8. 8.
    C. Di Franco, M. Paternostro, M. S. Kim, Phys. Rev. A 81, 022319 (2010)ADSCrossRefGoogle Scholar
  9. 9.
    A. O. Lyakhov, C. Bruder, Phys. Rev. B 74, 235303 (2006)ADSCrossRefGoogle Scholar
  10. 10.
    A. Wojcik, T. Luczak, P. Kurzynski, A. Grudka, T. Gdala, M. Bednarska, Phys. Rev. A 72, 034303 (2005)MathSciNetADSCrossRefGoogle Scholar
  11. 11.
    D. P. DiVincenzo, in Mesoscopic Electron Transport, eds. by L. Kowenhoven, G. Schön, L. Sohn (Kluwer, Dordrecht, 1997).Google Scholar
  12. 12.
    N. Gershenfeld, I. L. Chuang, Science 275, 350 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    S. L. Braunstein, C. M. Caves, R. Jozsa, N. Linden, S. Popescu, R. Schack, Phys. Rev. Lett. 83, 1054 (1999)ADSCrossRefGoogle Scholar
  14. 14.
    G. De Chiara, D. Rossini, S. Montangero, R. Fazio, Phys. Rev. A 72, 012323 (2005); D. Burgarth, Eur. Phys. J. Special Topics 151, 147 (2007); M. Wiesniak, arXiv:0711.2357; L. Zhou, J. Lu, T. Shi, C. P. Sun, arXiv:quant-ph/0608135Google Scholar
  15. 15.
    J. Fitzsimons, J. Twamley, Phys. Rev. Lett. 97, 090502 (2006)ADSCrossRefGoogle Scholar
  16. 16.
    C. Di Franco, M. Paternostro, M. S. Kim, Phys. Rev. Lett. 101, 230502 (2008); C. Di Franco, M. Paternostro, M. S. Kim, LNCS 6519, 168 (2011)Google Scholar
  17. 17.
    C. Di Franco, M. Paternostro, M. S. Kim, Phys. Rev. A 77, 020303(R) (2008)Google Scholar
  18. 18.
    D. M. Greenberger, M. A. Horne, A. Zeilinger, in Bell Theorem, Quantum Theory, and Conceptions of the Universe, ed. by M. Kafatos (Kluwer, Dordrecht, 1989)Google Scholar
  19. 19.
    E. Knill, R. Laflamme, Phys. Rev. Lett. 81, 5672 (1998)ADSCrossRefGoogle Scholar
  20. 20.
    S. Parker, M. B. Plenio, Phys. Rev. Lett. 85, 3049 (2000)ADSCrossRefGoogle Scholar
  21. 21.
    R. Raussendorf, H.-J. Briegel, Phys. Rev. Lett. 86, 5188 (2001)ADSCrossRefGoogle Scholar
  22. 22.
    M. Hein, J. Eisert, H.-J. Briegel, Phys. Rev. A 69, 062311 (2004); H.-J. Briegel, D. E. Browne, W. Dür, R. Raussendorf, M. Van den Nest, Nat. Phys. 5, 19 (2009)Google Scholar
  23. 23.
    M.-H. Yung, S. Bose, Phys. Rev. A 71, 032310 (2005); P. Karbach, J. Stolze, Phys. Rev. A 72, 030301(R) (2005)Google Scholar
  24. 24.
    T. J. G. Apollaro, A. Cuccoli, C. Di Franco, M. Paternostro, F. Plastina, P. Verrucchi, New J. Phys. 8, 083046 (2010)CrossRefGoogle Scholar
  25. 25.
    M. Markiewicz, M. Wiesniak, Phys. Rev. A 79, 054304 (2009); see also A. Kay, Int. J. Quant. Inf. 8, 641 (2010)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Carlo Di Franco
    • 1
    Email author
  • Mauro Paternostro
    • 1
  • M. S. Kim
    • 2
  1. 1.Centre for Theoretical Atomic, Molecular and Optical Physics, School of Mathematics and PhysicsQueen’s University BelfastBelfastUK
  2. 2.QOLS, Blackett Laboratory, Imperial College LondonLondonUK

Personalised recommendations