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Entanglement of Assistance

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Quantum Computing and Quantum Communications (QCQC 1998)

Abstract

The newfound importance of “ entanglement as a resource„ in quantum computation and quantum communication behooves us to quantify it in as many distinct ways as possible. Here we explore a new quantification of entanglement of a general (mixed) quantum state for a bipartite system, which we name entanglement of assistance. Weshowit to be the maximum of the average entanglement over all ensembles consistent with the density matrix describing the bipartite state. With the help of lower and upper bounds we calculate entanglement of assistance for a few cases and use these results to show the surprising property of superadditivity. We believe that this may throw some light on the question of additivity of entanglement of formation.

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References

  1. C.H. Bennett and G. Brassard “Quantum Cryptography: Public Key Distribution and Coin Tossing„, Proceedings of IEEE International Conference on Computers Systems and Signal Processing, Bangalore India, December 1984, pp 175–179.; D. Deutsch, A. Ekert, R. Jozsa, C. Macchiavello, S. Popescu, and A. Sanpera, Phys. Rev. Lett. 77, 2818 (1996).

    Google Scholar 

  2. C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, Phys. Rev. Lett. 70, 1895 (1993).

    Article  MATH  MathSciNet  Google Scholar 

  3. C. H. Bennett, C. A. Fuchs, and J. A. Smolin, “Entanglement-Enhanced Classical Communication on a Noisy Quantum Channel,„ in Quantum Communication, Computing and Measurement, edited by O. Hirota, A. S. Holevo, and C. M. Caves (Plenum, New York, 1997).

    Google Scholar 

  4. P. W. Shor, Phys. Rev. A 52, 2493 (1995); D. Gottesman, Ph. D. Thesis, California Institute of Technology, 1997, LANL e-print quant-ph/9705052.

    Google Scholar 

  5. R. Cleve and H. Buhrman, LANL e-print quant-ph/9704026.

    Google Scholar 

  6. J. J. Bollinger, W. M. Itano, D. J. Wineland, and D. J. Heinzen, Phys. Rev. A 54, R4649 (1996).

    Google Scholar 

  7. C.H. Bennet, D.P. DiVincenzo, J. A. Smolin, W.K. Wootters, Phys.Rev. A54, 3824 (1996), LANL e-print quant-ph/9604024.

    Google Scholar 

  8. C. H. Bennett, H. J. Bernstein, S. Popescu, B. Schumacher, Phys. Rev. A 53, 2046(1996), LANL e-print quant-ph/9511030.

    Google Scholar 

  9. L. P. Hughston, R. Jozsa, W. K. Wootters, Phys. Lett. A 183, 14 (1993).

    MathSciNet  Google Scholar 

  10. S. Hill, W. K. Wootters, Phys. Rev. Lett. 78, 5022 (1997), LANL e-print quant-ph/9703041.

    Article  Google Scholar 

  11. R. Jozsa, J. Mod. Opt. 41, 2315 (1994).

    MATH  Google Scholar 

  12. A. Uhlmann, Rep. Math. Phys. 9, 273 (1976).

    Article  MATH  MathSciNet  Google Scholar 

  13. C. A. Fuchs and J. van de Graaf, LANL e-print quant-ph/9712042.

    Google Scholar 

  14. R. Horodecki, M. Horodecki, Phys. Rev. A 54, 1838 (1996).

    Article  MathSciNet  Google Scholar 

  15. R. Horodecki, M. Horodecki, P. Horodecki, Phys. Lett. A 222, 21 (1996).

    Article  MATH  MathSciNet  Google Scholar 

  16. J. A. Smolin, private communication; W. K. Wootters, to appear in Phys. Rev. Lett., LANL e-print quant-ph/9709029.

    Google Scholar 

  17. M. Nielsen, private communication; The same result was independently conjectured in a discussion with C. H. Bennet and W. K. Wootters.

    Google Scholar 

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© 1999 Springer-Verlag Berlin Heidelberg

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DiVincenzo, D.P., Fuchs, C.A., Mabuchi, H., Smolin, J.A., Thapliyal, A., Uhlmann, A. (1999). Entanglement of Assistance. In: Williams, C.P. (eds) Quantum Computing and Quantum Communications. QCQC 1998. Lecture Notes in Computer Science, vol 1509. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49208-9_21

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  • DOI: https://doi.org/10.1007/3-540-49208-9_21

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  • Print ISBN: 978-3-540-65514-5

  • Online ISBN: 978-3-540-49208-5

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