Irreversibility of Entanglement Loss

  • Francesco Buscemi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5106)

Abstract

The action of a channel on a quantum system, when non trivial, always causes deterioration of initial quantum resources, understood as the entanglement initially shared by the input system with some reference purifying it. One effective way to measure such a deterioration is by measuring the loss of coherent information, namely the difference between the initial coherent information and the final one: such a difference is “small”, if and only if the action of the channel can be “almost perfectly” corrected with probability one.

In this work, we generalise this result to different entanglement loss functions, notably including the entanglement of formation loss, and prove that many inequivalent entanglement measures lead to equivalent conditions for approximate quantum error correction. In doing this, we show how different measures of bipartite entanglement give rise to corresponding distance-like functions between quantum channels, and we investigate how these induced distances are related to the cb-norm.

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References

  1. 1.
    Buscemi, F., Hayashi, M., Horodecki, M.: Phys. Rev. Lett. 100, 210504 (2008)Google Scholar
  2. 2.
    Gregoratti, M., Werner, R.F.: J. Mod. Opt.  50, 915 (2003); Buscemi, F., Chiribella, G., D’Ariano, G.M.: Phys. Rev. Lett. 95, 090501 (2005); Smolin, J.A., Verstraete, F., Winter, A.: Phys. Rev. A 72, 052317 (2005); Buscemi, F.: Phys. Rev. Lett. 99, 180501 (2007)Google Scholar
  3. 3.
    Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000); Kempe, J.: Quantum Decoherence. In: Poincaré Seminar 2005, Progress in Mathematical Physics Series. Birkhauser Verlag, Berlin (2006)Google Scholar
  4. 4.
    Buscemi, F.: Phys. Rev. A 77, 012309 (2008)Google Scholar
  5. 5.
    Kretschmann, D., Werner, R.F.: N. J. Phys.  6, 26 (2004)Google Scholar
  6. 6.
    Belavkin, V.P., D’Ariano, G.M., Raginsky, M.: J. Math. Phys. 46, 062106 (2005)Google Scholar
  7. 7.
    Christandl, M.: arXiv:quant-ph/0604183v1Google Scholar
  8. 8.
    Hayashi, M.: Quantum Information: an Introduction. Springer, Heidelberg (2006)MATHGoogle Scholar
  9. 9.
    Hayden, P., Leung, D.W., Winter, A.: Comm. Math. Phys. 265, 95 (2006)Google Scholar
  10. 10.
    Schumacher, B.: Phys. Rev. A 54, 2614 (1996)Google Scholar
  11. 11.
    Lloyd, S.: Phys. Rev. A 55, 1613 (1997)Google Scholar
  12. 12.
    Schumacher, B., Nielsen, M.A.: Phys. Rev. A 54, 2629 (1996)Google Scholar
  13. 13.
    Schumacher, B., Westmoreland, M.D.: Quant. Inf. Processing 1, 5 (2002)Google Scholar
  14. 14.
    Barnum, H., Nielsen, M.A., Schumacher, B.: Phys. Rev. A 57, 4153 (1998)Google Scholar
  15. 15.
    Hayden, P., Horodecki, M., Yard, J., Winter, A.: arXiv:quant-ph/0702005v1Google Scholar
  16. 16.
    Bennett, C.H., Di Vincenzo, D.P., Smolin, J.A., Wootters, W.K.: Phys. Rev. A 54, 3824 (1996)Google Scholar
  17. 17.
    Kretschmann, D., Schlingemann, D., Werner, R.F.: arXiv:quant-ph/0605009v1Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Francesco Buscemi
    • 1
  1. 1.ERATO-SORST Quantum Computation and Information Project, Japan Science and Technology AgencyJapan

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