Time-ordering dependence of measurements in teleportation

  • Reinhold A. Bertlmann
  • Heide Narnhofer
  • Walter Thirring
Regular Article

Abstract

We trace back the phenomenon of “delayed-choice entanglement swapping” as it was realized in a recent experiment to the commutativity of the projection operators that are involved in the corresponding measurement process. We also propose an experimental set-up which depends on the order of successive measurements corresponding to noncommutative projection operators. In this case entanglement swapping is used to teleport a quantum state from Alice to Bob, where Bob has now the possibility to examine the noncommutativity within the quantum history.

Keywords

Quantum Information 

References

  1. 1.
    X.-S. Ma, S. Zotter, J. Kofler, R. Ursin, T. Jennewein, C. Brukner, A. Zeilinger, Nat. Phys. 8, 480 (2012)CrossRefGoogle Scholar
  2. 2.
    A. Peres, J. Mod. Opt. 47, 139 (2000)MathSciNetADSGoogle Scholar
  3. 3.
    J. von Neumann, Mathematische Grundlagen der Quantenmechanik (Springer, 1996)Google Scholar
  4. 4.
    M. Gell-Mann, J.B. Hartle, Phys. Rev. D 47, 3345 (1993)MathSciNetADSCrossRefGoogle Scholar
  5. 5.
    R.B. Griffiths, Phys. Rev. A 54, 2759 (1996)ADSCrossRefGoogle Scholar
  6. 6.
    R.B. Griffiths, Phys. Rev. A 57, 1604 (1998)ADSCrossRefGoogle Scholar
  7. 7.
    A. Uhlmann, Antilinearity in Bipartite Quantum Systems and Imperfect Quantum Teleportation, in Quantum Probability and White Noise Analysis, Proceedings of the conference Quantum probability and infinite dimensional analysis, edited by W. Freudenberg (World Scientific, 2001), Vol. XV, p. 255Google Scholar
  8. 8.
    W. Thirring, R.A. Bertlmann, P. Köhler, H. Narnhofer, Eur. Phys. J. D 64, 181 (2011)ADSCrossRefGoogle Scholar
  9. 9.
    J.S. Bell, Physics 1, 195 (1964)Google Scholar
  10. 10.
    J.S. Bell, Speakable and Unspeakable of Quantum Mechanics (Cambridge University Press, 1987)Google Scholar
  11. 11.
    M. Horodecki, P. Horodecki, R. Horodecki, Phys. Lett. A 223, 1 (1996)MathSciNetADSMATHCrossRefGoogle Scholar
  12. 12.
    B.M. Terhal, Phys. Lett. A 271, 319 (2000)MathSciNetADSMATHCrossRefGoogle Scholar
  13. 13.
    R.A. Bertlmann, H. Narnhofer, W. Thirring, Phys. Rev. A 66, 032319 (2002)MathSciNetADSCrossRefGoogle Scholar
  14. 14.
    D. Bruß, J. Math. Phys. 43, 4237 (2002)MathSciNetADSMATHCrossRefGoogle Scholar
  15. 15.
    C.H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, W.K. Wootters, Phys. Rev. Lett. 70, 1895 (1993)MathSciNetADSMATHCrossRefGoogle Scholar
  16. 16.
    D. Bouwmeester, J.W. Pan, K. Mattle, M. Eibl, H. Weinfurter, A. Zeilinger, Nature 390, 575 (1997)ADSCrossRefGoogle Scholar
  17. 17.
    R. Ursin, T. Jennewein, M. Aspelmeyer, R. Kaltenbaek, M. Lindenthal, P. Walther, A. Zeilinger, Nature 430, 849 (2004)ADSCrossRefGoogle Scholar
  18. 18.
    A. Einstein, B. Podolsky, N. Rosen, Phys. Rev. A 47, 777 (1935)ADSMATHGoogle Scholar
  19. 19.
    M. Żukowski, A. Zeilinger, M. Horne, A. Ekert, Phys. Rev. Lett. 71, 4287 (1993)ADSCrossRefGoogle Scholar
  20. 20.
    J.-W. Pan, D. Bouwmeester, H. Weinfurter, A. Zeilinger, Phys. Rev. Lett. 80, 3891 (1998)MathSciNetADSMATHCrossRefGoogle Scholar
  21. 21.
    Quantum [Un]speakables, edited by R.A. Bertlmann, A. Zeilinger (Springer, 2002)Google Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Reinhold A. Bertlmann
    • 1
  • Heide Narnhofer
    • 1
  • Walter Thirring
    • 1
  1. 1.Faculty of PhysicsUniversity of ViennaViennaAustria

Personalised recommendations