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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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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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