Skip to main content
Log in

Is there a fundamental limit on the key distribution distance in quantum cryptography?

  • Published:
JETP Letters Aims and scope Submit manuscript

Abstract

Is there a fundamental limit on the key distribution distance in quantum cryptography? Are there quantum key distribution protocols approaching this limit and how close can they approach this limit? The answer to the first question is both yes and no. A general answer to the first question can be given without considering a particular quantum key distribution protocol and its implementation. The answer to the second question is given by a particular protocol for which the distribution distance is close to the theoretical limit and the achievement of this value is limited by our possibilities of correcting errors using classical codes rather than by the quantum key distribution protocol itself.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. C. H. Bennett and G. Brassard, in Proc. of IEEE Int. Conf. on Comput. Sys. and Sign. Process, Bangalore, India, Dec. 1984, p. 175.

  2. G. S. Vernam, J. Amer. Inst. Elect. Eng. 55, 109 (1926).

    Google Scholar 

  3. V. A. Kotelnikov, Report, June 18, 1941.

  4. C. E. Shannon, Bell Syst. Tech. J. 28, 658 (1949).

    Google Scholar 

  5. W. K. Wootters and W. H. Zurek, Nature 299, 802 (1982).

    Article  ADS  Google Scholar 

  6. C. H. Bennett, Phys. Rev. Lett. 68, 3121 (1992).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  7. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, Rev. Mod. Phys. 74, 145 (2002).

    Article  ADS  Google Scholar 

  8. V. Scarani, H. Btchmann-Pasquinucci, N. J. Cerf, et al., arXiv: [quant-ph] 0802.4155.

  9. I. Csiszár and J. Körner, IEEE Trns. Inf. Theory 24, 339(1978).

    Article  MATH  Google Scholar 

  10. B. Kraus, N. Gisin, and R. Renner, Phys. Rev. Lett. 95, 080501 (2005).

    Google Scholar 

  11. I. Devetak and A. Winter, Proc. Roy. Soc. A 461, 207(2005).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  12. C. E. Shannon, Bell Syst. Tech. J. 27, 397 (1948); Bell Syst. Tech. J. 27, 623 (1948).

    MathSciNet  Google Scholar 

  13. R. Gallager, Informanion Theory and Reliable Communication (Wiley, New York, 1968; Sovetskoe Radio, Moscow, 1974).

    Google Scholar 

  14. I. Csiszár and J. Körner, Information Theory: Coding Theorems for Discreter Memoryless Systems (Akademiai, Kiado, Budapest, 1981).

    Google Scholar 

  15. J. L. Carter and M. N. Wegman, J. Comp. System Sci. 18, 143 (1979).

    Article  MATH  MathSciNet  Google Scholar 

  16. C. H. Bennett, G. Brassard, C. Crépeau, and U. Maurer, IEEE Trans. Inform. Theory 41, 1915 (1995).

    Article  MATH  MathSciNet  Google Scholar 

  17. S. N. Molotkov, Pis’ma Zh. Éksp. Teor. Fiz. 88, 315(2008) [JETP Lett. 88, 275 (2008)].

    Google Scholar 

  18. G. Brassard and L. Salvail, Secret Key Reconciliation by Public Discussion, EUROCRYPT 410-423 (1993); Lect. Notes in Comp. Sci. 765, 410 (1994).

  19. E. J. Mac Williams and N. J. A. Sloane, The Theory of Error-Correcting Codes (North-Holland, Amsterdam, 1977).

    Google Scholar 

  20. W. W. Peterson and E. J. Weldon, Error-Correcting Codes (The MIT Press, Cambridge, Massachusetts, London, England, 1972).

    MATH  Google Scholar 

  21. R. H. Morelos-Zaragoza, The Art of Error Correcting Codes (Wiley, New York, 2002).

    Google Scholar 

  22. D. Mayers, J. Assoc. Comp. Mach. 48, 351 (2001).

    MathSciNet  Google Scholar 

  23. P. W. Shor and J. Preskill, Phys. Rev. Lett. 85, 441(2000).

    Article  ADS  Google Scholar 

  24. S. N. Molotkov and A. V. Timofeev, Pis’ma Zh. Éksp. Teor. Fiz. 85, 632 (2007) [JETP Lett. 85, 524 (2007)].

    Google Scholar 

  25. S. N. Molotkov, Zh. Éksp. Teor. Fiz. 133, 5 (2008) [JETP 106, 1 (2008)].

    Google Scholar 

  26. Book of Abstracts, Single-Photon Workshop 2007, Source, Detectors, Applications and Measurement Methods, Sept. 25–28, 2007, INRIM, Torino, Italy.

Download references

Author information

Authors and Affiliations

Authors

Additional information

Original Russian Text © S.N. Molotkov, 2008, published in Pis’ma v Zhurnal Éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2008, Vol. 88, No. 10, pp. 791–796.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Molotkov, S.N. Is there a fundamental limit on the key distribution distance in quantum cryptography?. Jetp Lett. 88, 693–697 (2008). https://doi.org/10.1134/S0021364008220128

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0021364008220128

PACS numbers

Navigation