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Concatenation of Keys in Quantum Cryptography: How Quantum Entanglement “Penetrates to” Classical Devices

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Abstract

Quantum mechanics admits collective measurements that are related to the projection onto entangled states and allow one to retrieve more classical information from an ensemble of quantum states compared with individual measurements. In this relation, a fundamental question arises for key secrecy in quantum cryptography. Should the secrecy criterion be formulated with regard to all keys distributed both on previous and future quantum key distribution (QKD) sessions, or it suffices to guarantee key secrecy only in an individual QKD session? The study of this question is the subject of the present paper.

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REFERENCES

  1. A. S. Holevo, Probl. Inf. Transm. 9, 177 (1973);

    Google Scholar 

  2. A. S. Kholevo, Usp. Mat. Nauk 53, 193 (1998);

    Article  Google Scholar 

  3. An Introduction to Quantum Information Theory, Vol. 5 of Modern Math. Phys. Ser. (MTsNMO, Moscow, 2002) [in Russian]; A. S. Kholevo, Quantum Systems, Channels, Information (MTsNMO, Moscow, 2010) [in Russian].

  4. E. Schrödinger, Naturwissensch. 23, 807 (1935).

    Article  ADS  Google Scholar 

  5. A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47, 777 (1935).

    Article  ADS  Google Scholar 

  6. J. S. Bell, Physics (Am. Phys. Soc.) 1, 195 (1964).

  7. A. Aspect, P. Grangier, and G. Roger, Phys. Rev. Lett. 49, 91 (1982).

    Article  ADS  Google Scholar 

  8. A. K. Ekert, Phys. Rev. Lett. 67, 661 (1991).

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  10. C. H. Bennett and S. Wiesner, Phys. Rev. Lett. 69, 2881 (1992).

    Article  ADS  MathSciNet  Google Scholar 

  11. M. Zukowski, A. Zeilinger, M. A. Horne, and A. K. Ekert, Phys. Rev. Lett. 71, 4287 (1993).

    Article  ADS  Google Scholar 

  12. B. Schumacher, Phys. Rev. A 51, 2738 (1995).

    Article  ADS  MathSciNet  Google Scholar 

  13. M. Tomamichel, Ch. Ci Wen Lim, N. Gisin, and R. Renner, Nat. Commun. 3, 1 (2012); arXiv:quant-ph/1103.4130 v2.

  14. M. Tomamichel and A. Leverrier, arXiv:quant-ph/1506.08458 V2.

  15. W. Heisenberg, Z. Phys. 43, 172 (1927).

    Article  ADS  Google Scholar 

  16. H. P. Robertson, Phys. Rev. 34, 163 (1929).

    Article  ADS  Google Scholar 

  17. R. Renner, PhD Thesis (ETH Zürich, 2005); arXiv:quant-ph/0512258.

  18. J. Müller-Quade and R. Renner, arXiv:quant-ph/1006.2215.

  19. C. Portmann and R. Renner, arXiv:quant-ph/1409.3525.

  20. M. M. Wilde, arXiv:quant-ph/1106.1445.

  21. H. P. Yuen, Phys. Rev. A 82, 062304 (2010).

    Article  ADS  Google Scholar 

  22. I. M. Arbekov and S. N. Molotkov, J. Exp. Theor. Phys. 125, 50 (2017).

    Article  ADS  Google Scholar 

  23. T. M. Cover and J. A. Thomas, Elements of Information Theory (Wiley, Chichester, 1991).

    Book  MATH  Google Scholar 

  24. T. Ogawa and H. Nagaoka, IEEE Trans. Inform. Theory 45, 2486 (1999).

    Article  MathSciNet  Google Scholar 

  25. R. G. Gallager, IEEE Trans. Inf. Theory 11, 3 (1965).

    Article  Google Scholar 

  26. S. Arimoto, IEEE Trans. Inf. Theory 19, 357 (1973).

    Article  Google Scholar 

  27. W. Roga, M. Fannes, and K. Zyczkowski, Phys. Rev. Lett. 105, 040505 (2010).

    Article  ADS  MathSciNet  Google Scholar 

  28. K. M. R. Audenaert, J. Math. Phys. 54, 073506 (2013);

    Article  ADS  MathSciNet  Google Scholar 

  29. J. Math. Phys. 55, 112202 (2014).

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ACKNOWLEDGMENTS

I am grateful to I.M. Arbekov, A.N. Klimov, and S.P. Kulik for numerous discussions, as well as to my colleagues from the Academy of Cryptography of the Russian Federation for constant support and discussions.

This work was supported by the Russian Science Foundation, project no. 16-12-00015.

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Correspondence to S. N. Molotkov.

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Translated by I. Nikitin

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Molotkov, S.N. Concatenation of Keys in Quantum Cryptography: How Quantum Entanglement “Penetrates to” Classical Devices. J. Exp. Theor. Phys. 127, 627–637 (2018). https://doi.org/10.1134/S1063776118090066

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  • DOI: https://doi.org/10.1134/S1063776118090066

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