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Quantum key distribution using gaussian-modulated coherent states


Quantum continuous variables1 are being explored2,3,4,5,6,7,8,9,10,11,12,13,14 as an alternative means to implement quantum key distribution, which is usually based on single photon counting15. The former approach is potentially advantageous because it should enable higher key distribution rates. Here we propose and experimentally demonstrate a quantum key distribution protocol based on the transmission of gaussian-modulated coherent states (consisting of laser pulses containing a few hundred photons) and shot-noise-limited homodyne detection; squeezed or entangled beams are not required13. Complete secret key extraction is achieved using a reverse reconciliation14 technique followed by privacy amplification. The reverse reconciliation technique is in principle secure for any value of the line transmission, against gaussian individual attacks based on entanglement and quantum memories. Our table-top experiment yields a net key transmission rate of about 1.7 megabits per second for a loss-free line, and 75 kilobits per second for a line with losses of 3.1 dB. We anticipate that the scheme should remain effective for lines with higher losses, particularly because the present limitations are essentially technical, so that significant margin for improvement is available on both the hardware and software.

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Figure 1: Experimental set-up.
Figure 2: Bob's measured quadrature as a function of the amplitude sent by Alice (in Bob's measurement basis) for a burst of 60,000 pulses.
Figure 3: Channel equivalent noise χline as a function of line transmission G.
Figure 4: Values of IBA, IBE and IAE as a function of the line transmission G for V ≈ 40. Here, IBA is given by equation (4a), including all transmission and detection noises for evaluating VB and (VB|A)coh.


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

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

    ADS  Article  Google Scholar 

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

    ADS  MathSciNet  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

  8. Van Assche, G., Cardinal, J. & Cerf, N. J. Reconciliation of a quantum-distributed Gaussian key. Preprint cs.CR/0107030 at 〈〉 (2001).

  9. Bencheikh, K., Symul, Th., Jankovic, A. & Levenson, J. A. Quantum key distribution with continuous variables. J. Mod. Opt. 48, 1903–1920 (2001)

    ADS  Article  Google Scholar 

  10. Cerf, N. J., Iblisdir, S. & Van Assche, G. Cloning and cryptography with quantum continuous variables. Eur. Phys. J. D 18, 211–218 (2002)

    ADS  MathSciNet  CAS  Google Scholar 

  11. Silberhorn, Ch., Korolkova, N. & Leuchs, G. Quantum key distribution with bright entangled beams. Phys. Rev. Lett. 88, 167902 (2002)

    ADS  Article  Google Scholar 

  12. 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)

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

  14. Grosshans, F. & Grangier, Ph. Reverse reconciliation protocols for quantum cryptography with continuous variables. Preprint quant-ph/0204127 at 〈〉 (2002).

  15. Gisin, N., Ribordy, G., Tittel, W. & Zbinden, H. Quantum cryptography. Rev. Mod. Phys. 74, 145–195 (2002)

    ADS  Article  Google Scholar 

  16. Cerf, N. J., Ipe, A. & Rottenberg, X. Cloning of continuous variables. Phys. Rev. Lett. 85, 1754–1757 (2000)

    ADS  CAS  Article  Google Scholar 

  17. Cerf, N. J. & Iblisdir, S. Optimal N-to-M cloning of conjugate quantum variables. Phys. Rev. A 62, 040301(R) (2000)

    ADS  MathSciNet  Article  Google Scholar 

  18. Grosshans, F. & Grangier, Ph. Quantum cloning and teleportation criteria for continuous quantum variables. Phys. Rev. A 64, 010301(R) (2001)

    ADS  MathSciNet  Article  Google Scholar 

  19. Bennett, C.-H. Quantum cryptography using any two nonorthogonal states. Phys. Rev. Lett. 68, 3121–3124 (1992)

    ADS  MathSciNet  CAS  Article  Google Scholar 

  20. Duan, L.-M., Giedke, G., Cirac, J. I. & Zoller, P. Entanglement purification of gaussian continuous variable quantum states. Phys. Rev. Lett. 84, 4002–4005 (2000)

    ADS  CAS  Article  Google Scholar 

  21. Csiszár, I. & Körner, J. Broadcast channel with confidential messages. IEEE Trans. Inform. Theory 24, 339–348 (1978)

    MathSciNet  Article  Google Scholar 

  22. Maurer, U. M. Secret key agreement by public discussion from common information. IEEE Trans. Inform. Theory 39, 733–742 (1993)

    MathSciNet  Article  Google Scholar 

  23. Poizat, J.-Ph., Roch, J.-F. & Grangier, Ph. Characterization of quantum non-demolition measurements in optics. Ann. Phys. (Paris) 19, 265–297 (1994)

    ADS  Google Scholar 

  24. Grangier, Ph., Levenson, J. A. & Poizat, J.-Ph. Quantum non-demolition measurements in optics. Nature 396, 537–542 (1998)

    ADS  CAS  Article  Google Scholar 

  25. Shannon, C. E. A mathematical theory of communication. Bell Syst. Tech. J. 27, 623–656 (1948)

    MathSciNet  Article  Google Scholar 

  26. Buttler, W. T., Lamoreaux, S. K., Torgerson, J. R., Nickel, G. H. & Peterson, C. G. Fast, efficient error reconciliation for quantum cryptography. Preprint quant-ph/0203096 at 〈〉 (2002).

  27. Brassard, G. & Salvail, L. Advances in Cryptology — Eurocrypt '93 Lecture Notes in Computer Science (ed. Helleseth, T.) 411–423 (Springer, New York, 1993)

    Google Scholar 

  28. Nguyen, K. Extension des Protocoles de Réconciliation en Cryptographie Quantique Thesis, Univ. Libre de Bruxelles (2002)

    Google Scholar 

  29. Lo, H.-K. Method for decoupling error correction from privacy amplification. Preprint quant-ph/0201030 at 〈〉 (2002)

  30. Bennett, C. H., Brassard, G., Crépeau, C. & Maurer, U. M. Generalized privacy amplification. IEEE Trans. Inform. Theory 41, 1915–1935 (1995)

    MathSciNet  Article  Google Scholar 

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The contributions of J. Gao to the early stages of the experiment, and of K. Nguyen to the software development, are acknowledged. We thank S. Iblisdir for discussions, and Th. Debuisschert for the loan of the 780 nm integrated modulator. This work was supported by the EU programme IST/FET/QIPC (projects “QUICOV” and “EQUIP”), the French programmes ACI Photonique and ASTRE, and by the Belgian programme ARC.

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Correspondence to Philippe Grangier.

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Grosshans, F., Van Assche, G., Wenger, J. et al. Quantum key distribution using gaussian-modulated coherent states. Nature 421, 238–241 (2003).

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