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Quantum Information: Entanglement, Purification, Error Correction, and Quantum Optical Implementations

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Fundamentals of Quantum Information

Part of the book series: Lecture Notes in Physics ((LNP,volume 587))

Abstract

It is generally recognized that all the microscopic phenomena that we observe can be described and explained by the principles of Quantum Mechanics. These principles have been extensively tested, and some of them are commonly used in several technological applications. Other principles, like the ones related to the measurement process and the superposition principle, have only recently become important in some applications. In particular, they form the basis of what is called quantum communication and quantum computation. These two fields have been strongly developed during the last few years, and they may well give rise to a technological revolution in the fields of communication and computation [1].

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References

  1. See, for example, Nielsen and Chuang Quantum computation and quantum information, (Cambridge University Press, Cambridge, 2000); The Physics of Quantum Information: Quantum Cryptography, Quantum Teleportation, Quantum Computation, Edited by D. Bouwmeester, A. Ekert and A. Zeilinger (Springer-Verlag, Berlin, 2000).

    Google Scholar 

  2. See, for example, D. P. DiVincenzo, Fortschr. Phys. 48, 771 (2000).

    Article  Google Scholar 

  3. J. I. Cirac and P. Zoller, Phys. Rev. Lett. 74 4091 (1995).

    Article  ADS  Google Scholar 

  4. J. F. Poyatos, J. I. Cirac and P. Zoller, Phys. Rev. Lett. 81 1322 (1998).

    Article  ADS  Google Scholar 

  5. J. I. Cirac and P. Zoller, Nature 404 579 (2000); T. Calarco, J.I. Cirac and P. Zoller, Phys. Rev. A (in press), quant-ph/0010105.

    Article  ADS  Google Scholar 

  6. A. Sorensen and K. Molmer, Phys. Rev. Lett. 82, 1971 (1999).

    Article  ADS  Google Scholar 

  7. K. Molmer and A. Sorensen, Phys. Rev. Lett. 82, 1835 (1999).

    Article  ADS  Google Scholar 

  8. S. Schneider, D. F. V. James, and G. J. Milburn, J. Mod. Opt. 47, 499 (2000).

    ADS  MathSciNet  Google Scholar 

  9. D. Jonathan and M. B. Plenio, quant-ph/0103140.

    Google Scholar 

  10. C. Monroe et al, Phys. Rev. Lett. 75 4714 (1995).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  11. C. A. Sackett et al., Nature 404, 256 (2000).

    Article  ADS  Google Scholar 

  12. M. A. Rowe et al., Nature 409, 791 (2001).

    Article  Google Scholar 

  13. Ch. Roos et al., Phys. Rev. Lett. 83, 4713 (1999).

    Article  ADS  Google Scholar 

  14. T. Sleator and H. Weinfuhrter, Phys. Rev. Lett. 74, 4087 (1995)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  15. T. Pellizari, et al., Phys. Rev. Lett. 75, 3788 (1995).

    Article  ADS  Google Scholar 

  16. Q. A. Turchette et al, Phys. Rev. Lett. 75 4710 (1995).

    Article  ADS  MathSciNet  Google Scholar 

  17. X. Maître et al, Phys. Rev. Lett. 79 769 (1997).

    Article  ADS  Google Scholar 

  18. Rauschenbeutel, A. et al., Science 288, 2024 (2000).

    Article  ADS  Google Scholar 

  19. S. Brattke et al., Phys. Rev. Lett. 86, 3534 (2001).

    Article  ADS  Google Scholar 

  20. D. Jaksch et al., Phys. Rev. Lett. 82, 1975 (1999); T. Calarco et al., Phys. Rev. A 61, 022304 (2000).

    Article  ADS  Google Scholar 

  21. D. Jaksch et al., Phys. Rev. Lett. 85, 2208 (2000).

    Article  ADS  Google Scholar 

  22. G. K. Brennen et al., Phys. Rev. Lett. 82, 1060 (1999).

    Article  ADS  Google Scholar 

  23. A. Beige et al., J.Mod.Opt. 47, 401 (2000).

    ADS  MathSciNet  Google Scholar 

  24. B. E. Kane, Nature 393 133 (1998).

    Article  ADS  Google Scholar 

  25. D. Loss and D. P. DiVincenzo, Phys. Rev. A 57, 120 (1998).

    ADS  Google Scholar 

  26. Y. Makhlin and G. Schön, Nature 398, 305 (1999).

    Article  ADS  Google Scholar 

  27. D. G. Cory, A. F. Fahmy and T. F. Havel, Proc. Natl. Acad. Sci. 94 1634 (1997).

    Article  ADS  Google Scholar 

  28. N. A. Gershenfeld and I. L. Chuang, Science 275 350, (1997).

    Article  MathSciNet  Google Scholar 

  29. S. L. Braunstein et al., Linden,... Phys. Rev. Lett. 83, 1054 (1999)

    Article  ADS  Google Scholar 

  30. See, for example, D. F. James, Fortschr. Phys. 48, 823 (2000); see also, A. M. Steane and D. M. Lucas, Fortschr. Phys. 48, 839 (2000).

    Article  Google Scholar 

  31. P. W. Shor, Phys. Rev. A 52 2493 (1995).

    ADS  Google Scholar 

  32. A. M. Steane, Phys. Rev. Lett. 77 793 (1996).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  33. R. Laflamme et al., Phys. Rev. Lett. 77, 198–201 (1996).

    Article  ADS  Google Scholar 

  34. D. Gottesman, Phys. Rev. A 54, 1862–1868 (1996)

    ADS  MathSciNet  Google Scholar 

  35. P. Shor, in 37th Symposium on Foundations of Computing, IEEE Computer Society Press, pp. 56–65 (1996).

    Google Scholar 

  36. J. I. Cirac, T. Pellizari and P. Zoller, Science 273, 1207 (1996).

    Article  ADS  Google Scholar 

  37. D. Gottesman, Phys. Rev. A 57, 127 (1998)

    ADS  Google Scholar 

  38. J. Preskill, Proc. R. Soc. 454 385 (1998).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  39. A. Steane, Fortsch.Phys. 46, 443 (1998).

    Article  ADS  MathSciNet  Google Scholar 

  40. J. S. Bell, Physics 1, 195 (1964).

    Google Scholar 

  41. C. H. Bennett et al., Phys. Rev. A 53, 2046 (1996).

    ADS  Google Scholar 

  42. S. Popescu and D. Rohrlich, Phys. Rev. A 56 3319 (1997).

    ADS  MathSciNet  Google Scholar 

  43. D. M. Greenberger, M. Horne, and A. Zeilinger, in Bell’s theorem, Quantum Theory and Conceptions of the Universe, edited by M. Kafatos (Kluwer Academic, Dordrecht, The Netherlands, 1989), pp 69.

    Google Scholar 

  44. N. Linden and S. Popescu, Fortsch.Phys. 46, 567 (1998).

    Article  ADS  MathSciNet  Google Scholar 

  45. G. Giedke et al., quant-ph/0104050.

    Google Scholar 

  46. W. Dür, G. Vidal, and J. I. Cirac, Phys. Rev. A 62, 62314 (2000).

    Google Scholar 

  47. R. F. Werner, Phys. Rev. A 40, 4277 (1989).

    ADS  Google Scholar 

  48. M. Lewenstein et al., J. Mod. Opt. 77, 2481 (2000).

    ADS  MathSciNet  Google Scholar 

  49. B. M. Terhal, quant-ph/0101032.

    Google Scholar 

  50. R. Horodecki, P. Horodecki, M. Horodecki, Phys. Lett. A 210 377 (1996).

    ADS  MathSciNet  Google Scholar 

  51. J.F. Clauser et al., Phys. Rev. Lett. 23, 880 (1969).

    Article  ADS  Google Scholar 

  52. See, for example, W. Rudin, Functional analysis (Mac Graw-Hill, New York, 1991).

    MATH  Google Scholar 

  53. E. Stromer, Acta Math. 110, 233 (1963).

    Article  MathSciNet  Google Scholar 

  54. S. L. Woronowicz, Rep. Math. Phys. 10, 165 (1976).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  55. B. M. Terhal, quant-ph/9810091; see also quant-ph/9911057.

    Google Scholar 

  56. M. Lewenstein et al., Phys. Rev. A 62, 52310 (2000).

    ADS  MathSciNet  Google Scholar 

  57. M. Lewenstein et al., quant-ph/0005112.

    Google Scholar 

  58. A. Jamiolkowski, Rep. of Math. Phy. No. 4, 3 (1972).

    Google Scholar 

  59. A. Peres, Phys. Rev. Lett 77, 1413 (1996).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  60. P. Horodecki, Phys. Lett. A 232, 333 (1997).

    ADS  MathSciNet  Google Scholar 

  61. C. H. Bennett et al., 82, 5385 (1999).

    Google Scholar 

  62. P. Horodecki and M. Lewenstein, Phys. Rev. Lett. 85, 2657 (2000).

    Article  ADS  MathSciNet  Google Scholar 

  63. R. F. Werner and M. M. Wolf, Phys. Rev. Lett. 86, 3658 (2001).

    Article  ADS  Google Scholar 

  64. D. Bruss and A. Peres, Phys. Rev. A 61, 030301 (2000).

    ADS  MathSciNet  Google Scholar 

  65. B. Kraus et al. Phys. Rev. A 61, 062302 (2000).

    ADS  MathSciNet  Google Scholar 

  66. W. Dür, J. I. Cirac, and R. Tarrach, Phys. Rev. Lett. 83, 3562 (1999); W. Dür and J. I. Cirac, Phys. Rev. A 61, 042314 (2000).

    Article  ADS  Google Scholar 

  67. C. H. Bennett et al., Phys. Rev. Lett. 76, 722 (1996); C. H. Bennett, et al., Phys.Rev. A 54, 3824 (1996).

    Article  ADS  Google Scholar 

  68. N. Gisin, Phys. Lett. A 210, 151 (1996).

    ADS  MathSciNet  Google Scholar 

  69. H.-K. Lo and S. Popescu, Phys. Rev. A 63, 022301 (2001).

    ADS  Google Scholar 

  70. M. A. Nielsen, Phys. Rev. Lett. 83, 436 (1999).

    Article  ADS  Google Scholar 

  71. G. Vidal, Phys.Rev.Lett. 83, 1046 (1999).

    Article  ADS  Google Scholar 

  72. D. Jonathan, M. B. Plenio, Phys. Rev. Lett. 83, 1455 (1999); see also erratum Phys. Rev. Lett. 84, 4781 (2000).

    Article  ADS  MathSciNet  Google Scholar 

  73. L. Hardy, Phys. Rev. A 60, 1912 (1999)

    ADS  MathSciNet  Google Scholar 

  74. E. M. Rains, Phys. Rev. A 60, 173 (1999).

    ADS  MathSciNet  Google Scholar 

  75. E. M. Rains, Phys. Rev. A 60, 179 (1999).

    ADS  MathSciNet  Google Scholar 

  76. David Deutsch et al., Phys. Rev. Lett. 77, 2818 (1996).

    Article  ADS  Google Scholar 

  77. M. Horodecki, P. Horodecki, and R. Horodecki, Phys. Rev. Lett. 80, 5239 (1998).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  78. G. Giedke et al., quant-ph/0104072.

    Google Scholar 

  79. D. DiVincenzo et al., Phys. Rev. A 61, 62312 (2000).

    Google Scholar 

  80. W. Dür et al., Phys. Rev. A 61, 62313 (2000).

    ADS  Google Scholar 

  81. W. Dür and J. I. Cirac, Phys. Rev. A 62, 22302 (2000).

    Google Scholar 

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Cirac, J.I. (2002). Quantum Information: Entanglement, Purification, Error Correction, and Quantum Optical Implementations. In: Heiss, D. (eds) Fundamentals of Quantum Information. Lecture Notes in Physics, vol 587. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45933-2_6

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  • DOI: https://doi.org/10.1007/3-540-45933-2_6

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