Skip to main content
SpringerLink
Log in

Performance analysis of continuous-variable quantum key distribution using non-Gaussian states

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

In this study, we analyse the efficiency of a protocol with discrete modulation of continuous variable non-Gaussian states, that is, the coherent states having the addition of one photon followed by the subtraction of one photon (PASCS). We calculate lower bounds of the asymptotic key rates against Gaussian collective attacks based on the fact that for sufficiently small modulation variances we remain close to the protocol with Gaussian modulation. We compare the results of a four-state protocol (quadrature phase-shift-keying) using PASCS with the ones using coherent states, and show that under the same environmental conditions, the former always outperforms the latter, allowing to increase the maximum possible distance for secret key generation. Interestingly, we find that for the protocol using discrete-modulated PASCS, the noisier the line, the better will be its performance compared to the protocol using coherent states, showing that continuous variable non-Gaussian states can be considerably more advantageous for performing quantum key distribution in non-ideal situations.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

Data availability

The manuscript has no associated data.

References

  1. Grosshans, F., Grangier, P.: Continuous variable quantum cryptography using coherent states. Phys. Rev. Lett. 88, 057902 (2002)

    Article  ADS  Google Scholar 

  2. Silberhorn, Ch., Ralph, T.C., Lütkenhaus, N., Leuchs, G.: Continuous variable quantum cryptography: beating the 3 dB loss limit. Phys. Rev. Lett. 89, 167901 (2002)

    Article  ADS  Google Scholar 

  3. Grosshans, F., Grangier, P.: Reverse reconciliation protocols for quantum cryptography with continuous variables. arXiv preprint arXiv:quant-ph/0204127 (2002)

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

    Article  ADS  Google Scholar 

  5. Christandl, M., Renner, R., Ekert, A.: arXiv:quant-ph/0402131 (2004)

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

    Article  ADS  Google Scholar 

  7. Lodewyck, J., et al.: Quantum key distribution over 25 km with an all-fiber continuous-variable system. Phys. Rev. A 76, 042305 (2007)

    Article  ADS  Google Scholar 

  8. Jouguet, P., et al.: Experimental demonstration of long-distance continuous-variable quantum key distribution. Nat. Photonics 7, 378 (2013)

    Article  ADS  Google Scholar 

  9. Namiki, R., Hirano, T.: Security of quantum cryptography using balanced homodyne detection. Phys. Rev. A 67, 022308 (2003)

    Article  ADS  Google Scholar 

  10. Leverrier, A., Grangier, P.: Unconditional security proof of long-distance continuous-variable quantum key distribution with discrete modulation. Phys. Rev. Lett. 102, 180504 (2009)

    Article  ADS  Google Scholar 

  11. Leverrier, A., Grangier, P.: Erratum: Unconditional security proof of long-distance continuous-variable quantum key distribution with discrete modulation. Phys. Rev. Lett. 106, 259902 (2011)

    Article  ADS  Google Scholar 

  12. Leverrier, A., Grangier, P.: Continuous-variable quantum-key-distribution protocols with a non-Gaussian modulation. Phys. Rev. A 83, 042312 (2011)

    Article  ADS  Google Scholar 

  13. Ghorai, S., Grangier, P., Diamanti, E., Leverrier, A.: Asymptotic security of continuous-variable quantum key distribution with a discrete modulation. Phys. Rev. X 9, 021059 (2019)

    Google Scholar 

  14. Lin, J., Upadhyaya, T., Lütkenhaus, N.: Asymptotic security analysis of discrete-modulated continuous-variable quantum key distribution. Phys. Rev. X 9, 041064 (2019)

    Google Scholar 

  15. Denys, A., Brown, P., Leverrier, A.: Explicit asymptotic secret key rate of continuous variable quantum key distribution with an arbitrary modulation. Quantum 5, 540 (2021)

    Article  Google Scholar 

  16. Leverrier, A. et al.: Quantum communications with Gaussian and non-Gaussian states of light In: International Conference on Quantum Information, OSA Technical Digest (CD) (Optical Society of America, 2011), paper QMF1. http://www.opticsinfobase.org/abstract.cfm?URI=ICQI-2011-QMF1

  17. Becir, A., Wahiddin, M.R.: Phase coherent states for enhancing the performance of continuous variable quantum key distribution. J. Phys. Soc. Jpn. 81, 034005 (2012)

    Article  ADS  Google Scholar 

  18. Borelli, L.F.M., Aguiar, L.S., Roversi, J.A., Vidiella-Barranco, A.: Quantum key distribution using continuous-variable non-Gaussian states. Quantum Inf. Process. 15, 893–904 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  19. Srikara, S., Tapliyal, K., Pathak, A.: Continuous variable B92 quantum key distribution protocol using single photon added and subtracted coherent states. Quantum Inf. Process. 19, 371 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  20. Li, F., Wang, Y., Liao, Q., Guo, Y.: Four-state continuous-variable quantum key distribution with photon subtraction. Int. J. Theor. Phys. 57, 2755 (2018)

    Article  MathSciNet  Google Scholar 

  21. Ghalaii, M., Ottaviani, C., Kumar, R., Pirandola, S., Razavi, M.S.: Discrete-modulation continuous-variable quantum key distribution enhanced by quantum scissors. IEEE J. Sel. Areas Commun. 38, 506 (2020)

    Article  Google Scholar 

  22. Pariggi, V., Zavatta, A., Kim, M., Bellini, M.: Probing quantum commutation rules by addition and subtraction of single photons to/from a light field. Science 317, 1890 (2007)

    Article  ADS  Google Scholar 

  23. Wang, Z., Yuan, H., Fan, H.: Nonclassicality of the photon addition-then-subtraction coherent state and its decoherence in the photon-loss channel. J. Opt. Soc. Am. B 28, 1964 (2011)

    Article  ADS  Google Scholar 

  24. 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 

  25. 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 

  26. Grosshans, F., et al.: Virtual entanglement and reconciliation protocols for quantum cryptography with continuous variables. Quantum Inf. Comput. 3, 535–552 (2003)

    MathSciNet  MATH  Google Scholar 

  27. Shannon, C.E.: A mathematical theory of communication. Bell Syst. Tech. J. 27, 379 (1948)

    Article  MathSciNet  Google Scholar 

  28. Zhao, W., et al.: Unidimensional continuous-variable quantum key distribution with discrete modulation. Phys. Lett. A 384, 126061 (2020)

    Article  MathSciNet  Google Scholar 

  29. Wang, X., et al.: Realistic rate-distance limit of continuous-variable quantum key distribution. Opt. Express 27, 13372 (2019)

    Article  ADS  Google Scholar 

  30. Zavatta, A., Fiurášek, J., Bellini, M.: A high-fidelity noiseless amplifier for quantum light states. Nat. Photonics 5, 52 (2011)

    Article  ADS  Google Scholar 

  31. Blandino, R., Leverrier, A., Barbieri, M., Etesse, J., Grangier, P., Tualle-Brouri, R.: Improving the maximum transmission distance of continuous-variable quantum key distribution using a noiseless amplifier. Phys. Rev. A 86, 012327 (2012)

    Article  ADS  Google Scholar 

  32. Walk, N., Ralph, T.C., Symul, T., Lam, P.K.: Security of continuous-variable quantum cryptography with Gaussian postselection. Phys. Rev. A 87, 020303(R) (2013)

    Article  ADS  Google Scholar 

  33. Fiurasek, J., Cerf, N.J.: Gaussian postselection and virtual noiseless amplification in continuous-variable quantum key distribution. Phys. Rev. A 86, 060302(R) (2012)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This work has been supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico, (CNPq) Brazil, via the Instituto Nacional de Ciência e Tecnologia - Informação quântica (INCT-IQ), grant N\({^{\underline{o}}}\) 465469/2014-0.

Author information

Authors and Affiliations

  1. “Gleb Wataghin” Institute of Physics, University of Campinas, Campinas, SP, 13083-859, Brazil

    L. S. Aguiar, L. F. M. Borelli, J. A. Roversi & A. Vidiella-Barranco

Authors
  1. L. S. Aguiar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. F. M. Borelli
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J. A. Roversi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. A. Vidiella-Barranco
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. Vidiella-Barranco.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Aguiar, L.S., Borelli, L.F.M., Roversi, J.A. et al. Performance analysis of continuous-variable quantum key distribution using non-Gaussian states. Quantum Inf Process 21, 304 (2022). https://doi.org/10.1007/s11128-022-03645-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-022-03645-z

Keywords

Search

Navigation