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Continuous-variable quantum cryptography using two-way quantum communication

Nature Physics volume 4, pages 726–730 (2008)Cite this article

Abstract

Quantum cryptography has recently been extended to continuous-variable systems, such as the bosonic modes of the electromagnetic field possessing continuous degrees of freedom. In particular, several cryptographic protocols have been proposed and experimentally implemented using bosonic modes with Gaussian statistics. These protocols have shown the possibility of reaching very high secret key rates, even in the presence of strong losses in the quantum communication channel. Despite this robustness to loss, their security can be affected by more general attacks where extra Gaussian noise is introduced by the eavesdropper. Here, we show a ‘hardware solution’ for enhancing the security thresholds of these protocols. This is possible by extending them to two-way quantum communication where subsequent uses of the quantum channel are suitably combined. In the resulting two-way schemes, one of the honest parties assists the secret encoding of the other, with the chance of a non-trivial superadditive enhancement of the security thresholds. These results should enable the extension of quantum cryptography to more complex quantum communications.

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Figure 1: Coherent-state protocols.
Figure 2: Security thresholds in direct reconciliation.
Figure 3: Security thresholds in reverse reconciliation.
Figure 4: General structure of the one-way, two-way and hybrid protocols, together with their possible collective attacks.
Figure 5: Two-way quantum communication scheme.

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References

  1. Braunstein, S. L. & Pati, A. K. Quantum Information Theory with Continuous Variables (Kluwer–Academic, Dordrecht, 2003).

    Book  Google Scholar 

  2. Braunstein, S. L. & van Loock, P. Quantum information with continuous variables. Rev. Mod. Phys. 77, 513–577 (2005).

    Article  ADS  MathSciNet  Google Scholar 

  3. Eisert, J. & Plenio, M. B. Introduction to the basics of entanglement theory in continuous-variable systems. Int. J. Quantum Inf. 1, 479–506 (2003).

    Article  Google Scholar 

  4. Ferraro, A., Olivares, S. & Paris, M. G. A. Gaussian States in Quantum Information (Bibliopolis, Napoli, 2005).

    Google Scholar 

  5. Hillery, M. Quantum cryptography with squeezed states. Phys. Rev. A 61, 022309 (2000).

    Article  ADS  Google Scholar 

  6. Ralph, T. C. Continuous variable quantum cryptography. Phys. Rev. A 61, 010303(R) (2000).

    Article  ADS  MathSciNet  Google Scholar 

  7. Ralph, T. C. Security of continuous-variable quantum cryptography. Phys. Rev. A 62, 062306 (2000).

    Article  ADS  Google Scholar 

  8. Reid, M. D. Quantum cryptography with a predetermined key, using continuous-variable Einstein–Podolsky–Rosen correlations. Phys. Rev. A 62, 062308 (2000).

    Article  ADS  Google Scholar 

  9. Gottesman, D. & Preskill, J. Secure quantum key distribution using squeezed states. Phys. Rev. A 63, 022309 (2001).

    Article  ADS  Google Scholar 

  10. Cerf, N. J., Lévy, M. & Van Assche, G. Quantum distribution of Gaussian keys using squeezed states. Phys. Rev. A 63, 052311 (2001).

    Article  ADS  Google Scholar 

  11. Grosshans, F. & Grangier, Ph. Continuous variable quantum cryptography using coherent states. Phys. Rev. Lett. 88, 057902 (2002).

    Article  ADS  Google Scholar 

  12. Grosshans, F. et al. Quantum key distribution using Gaussian-modulated coherent states. Nature 421, 238–241 (2003).

    Article  ADS  Google Scholar 

  13. Iblisdir, S., Van Assche, G. & Cerf, N. J. Security of quantum key distribution with coherent states and homodyne detection. Phys. Rev. Lett. 93, 170502 (2004).

    Article  ADS  Google Scholar 

  14. Grosshans, F. & Cerf, N. J. Continuous-variable quantum cryptography is secure against non-Gaussian attacks. Phys. Rev. Lett. 92, 047905 (2004).

    Article  ADS  Google Scholar 

  15. Weedbrook, C. et al. Quantum cryptography without switching. Phys. Rev. Lett. 93, 170504 (2004).

    Article  ADS  Google Scholar 

  16. Lance, A. M. et al. No-switching quantum key distribution using broadband modulated coherent light. Phys. Rev. Lett. 95, 180503 (2005).

    Article  ADS  Google Scholar 

  17. Silberhorn, Ch. et al. Continuous variable quantum cryptography: Beating the 3 dB loss limit. Phys. Rev. Lett. 89, 167901 (2002).

    Article  ADS  Google Scholar 

  18. Namiki, R. & Hirano, T. Practical limitation for continuous-variable quantum cryptography using coherent states. Phys. Rev. Lett. 92, 117901 (2004).

    Article  ADS  Google Scholar 

  19. Namiki, R. & Hirano, T. Security of continuous-variable quantum cryptography using coherent states: Decline of postselection advantage. Phys. Rev. A 72, 024301 (2005).

    Article  ADS  Google Scholar 

  20. Namiki, R. & Hirano, T. Efficient-phase-encoding protocols for continuous-variable quantum key distribution using coherent states and postselection. Phys. Rev. A 74, 032302 (2006).

    Article  ADS  Google Scholar 

  21. Heid, M. & Lütkenhaus, N. Efficiency of coherent-state quantum cryptography in the presence of loss: Influence of realistic error correction. Phys. Rev. A 73, 052316 (2006).

    Article  ADS  Google Scholar 

  22. Grosshans, F., Cerf, N. J., Wenger, J., Tualle-Brouri, R. & Grangier, Ph. Virtual entanglement and reconciliation protocols for quantum cryptography with continuous variables. Quantum. Inf. Comput. 3, 535–552 (2003).

    MathSciNet  MATH  Google Scholar 

  23. Van Assche, G., Cardinal, J. & Cerf, N. J. Reconciliation of a quantum-distributed Gaussian key. IEEE Trans. Inf. Theory 50, 394–400 (2004).

    Article  MathSciNet  Google Scholar 

  24. Navascués, M., Grosshans, F. & Acín, A. Optimality of Gaussian attacks in continuous-variable quantum cryptography. Phys. Rev. Lett. 97, 190502 (2006).

    Article  ADS  Google Scholar 

  25. García-Patrón, R. & Cerf, N. J. Unconditional optimality of Gaussian attacks against continuous-variable quantum key distribution. Phys. Rev. Lett. 97, 190503 (2006).

    Article  ADS  Google Scholar 

  26. Renner, R., Gisin, N. & Kraus, B. Information-theoretic security proof for quantum-key-distribution protocols. Phys. Rev. A 72, 012332 (2005).

    Article  ADS  Google Scholar 

  27. Renner, R. Security of Quantum Key Distribution. PhD thesis, Swiss Federal Institute of Technology (ETH) Zurich (2005).

  28. Lodewyck, J. & Grangier, Ph. Tight bound on coherent states quantum key distribution with heterodyne detection. Phys. Rev. A 76, 022332 (2007).

    Article  ADS  Google Scholar 

  29. Sudjana, J., Magnin, L., García-Patrón, R. & Cerf, N. J. Tight bounds on the eavesdropping of a continuous-variable quantum cryptographic protocol with no basis switching. Phys. Rev. A 76, 052301 (2007).

    Article  ADS  Google Scholar 

  30. Grosshans, F. Collective attacks and unconditional security in continuous variable quantum key distribution. Phys. Rev. Lett. 94, 020504 (2005).

    Article  ADS  Google Scholar 

  31. Navascués, M. & Acín, A. Security bounds for continuous variables quantum key distribution. Phys. Rev.Lett. 94, 020505 (2005).

    Article  ADS  Google Scholar 

  32. Dušek, M., Haderka, O., Hendrych, M. & Myška, R. Quantum identification system. Phys. Rev. A 60, 149–156 (1999).

    Article  ADS  Google Scholar 

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Acknowledgements

The research of S.P. was supported by a Marie Curie Outgoing International Fellowship within the 6th European Community Framework Programme (Contract No. MOIF-CT-2006-039703). S.P. thanks CNISM for hospitality at Università di Camerino and Gaetana Spedalieri for her moral and logistic support. S.L. was supported by the W.M. Keck centre for extreme quantum information processing (xQIT).

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Authors and Affiliations

  1. Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

    Stefano Pirandola & Seth Lloyd

  2. Dipartimento di Fisica & CNISM, Università di Camerino, Camerino 62032, Italy

    Stefano Mancini

  3. Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

    Seth Lloyd

  4. Department of Computer Science, University of York, York YO10 5DD, UK

    Samuel L. Braunstein

Authors
  1. Stefano Pirandola
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  2. Stefano Mancini
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  3. Seth Lloyd
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  4. Samuel L. Braunstein
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Correspondence to Stefano Pirandola.

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Pirandola, S., Mancini, S., Lloyd, S. et al. Continuous-variable quantum cryptography using two-way quantum communication. Nature Phys 4, 726–730 (2008). https://doi.org/10.1038/nphys1018

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