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The schmidt number of pure continuous-variable bipartite entangled states and the method of its calculation

  • Quantum Communications with Continuous Variable Coding
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Abstract

The Schmidt number—the measure of entanglement of pure states of a continuous-variable bipartite system—is analytically calculated for a simple model of photon-atom scattering.

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References

  1. The Physics of Quantum Information, Ed. by Bouwmeester, A. Ekert, and A. Zeilinger (Springer, Berlin, 2000; Postmarket, Moscow, 2002).

    MATH  Google Scholar 

  2. R. Grobe, K. Rzazewski, and J. H. Eberly, J. Phys. B 27, L503 (1994).

    Article  ADS  Google Scholar 

  3. A. Ekert and P. L. Knight, Am. J. Phys 63(5), 415 (1995).

    Article  ADS  Google Scholar 

  4. J. H. Eberly, arXiv:quant-ph/0508019 (2005).

  5. J. P. Torres, F. Macia, S. Carrasco, and L. Torner, Opt. Lett. 30(3), 314 (2005).

    Article  ADS  Google Scholar 

  6. C. K. Law, Phys. Rev. A 7(6), 062311 (2004).

    Google Scholar 

  7. C. K. Law and J. H. Eberly, Phys. Rev. Lett. 92(12), 127903 (2004).

    Google Scholar 

  8. J. Wang, C. K. Law, and M.-C. Chu, Phys. Rev. A 73, 034302 (2006).

  9. S. K. Y. Lee and C. K. Law, Phys. Rev. A 73, 053808 (2006).

    Google Scholar 

  10. G. Adesso, A. Serafini, and F. Illuminati, Phys. Rev. A 70, 022318 (2004).

    Google Scholar 

  11. P. Holmes, J. L. Lumley, and G. Berkooz, Turbulence, Coherent Structures, Dynamical Systems, and Symmetry (Cambrige Univ. Press, Cambrige, 1996).

    MATH  Google Scholar 

  12. K. S. Fu, Sequential Methods in Pattern Recognition and Machine Learning (Academic, New York, 1968; Nauka, Moscow, 1971).

    MATH  Google Scholar 

  13. L. Lamata and J. Leon, J. Opt. B 7(8), 224 (2005).

    Google Scholar 

  14. C. Tsallis, J. Stat. Phys. 52(1/2), 479 (1988).

    Article  MATH  Google Scholar 

  15. V. V. Dodonov, J. Opt. B 4(3), 98 (2002).

    Google Scholar 

  16. M. Karelin, J. Phys. A 38(28), 6393 (2005).

    Article  MATH  Google Scholar 

  17. C. H. Bennett, H. J. Bernstein, S. Popescu, and B. Schumacher, Phys. Rev. A 53(4), 2046 (1996).

    Article  ADS  Google Scholar 

  18. G. Adesso, A. Serafini, and F. Illuminati, Phys. Rev. Lett. 92, 087901 (2004).

    Google Scholar 

  19. K. W. Chan, C. K. Law, and J. H. Eberly, Phys. Rev. Lett. 88(10), 100402 (2002).

    Google Scholar 

  20. J. H. Eberly, K. W. Chan, and C. K. Law, Chaos, Solitons, Fractals 16, 399 (2003).

    Article  MATH  Google Scholar 

  21. J. H. Eberly, K. W. Chan, and C. K. Law, Philos. Trans. R. Soc. London 361(1808), 1519 (2003).

    Article  ADS  Google Scholar 

  22. K. W. Chan, C. K. Law, and J. H. Eberly, Phys. Rev. A 68(2), 022110 (2003).

  23. R. Guo and H. Guo, Phys. Rev. A 73, 012103 (2006).

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Correspondence to M. U. Karelin.

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Original Russian Text © M.U. Karelin, 2007, published in Optika i Spektroskopiya, 2007, Vol. 103, No. 2, pp. 201–203.

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Karelin, M.U. The schmidt number of pure continuous-variable bipartite entangled states and the method of its calculation. Opt. Spectrosc. 103, 193–195 (2007). https://doi.org/10.1134/S0030400X07080048

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  • DOI: https://doi.org/10.1134/S0030400X07080048

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