## A 24 km fiber-based discretely signaled continuous variable quantum key distribution system

Optics Express, Vol. 17, Issue 26, pp. 24244-24249 (2009)

http://dx.doi.org/10.1364/OE.17.024244

Acrobat PDF (279 KB)

### Abstract

We report a continuous variable key distribution system that achieves a final secure key rate of 3.45 kilobits/s over a distance of 24.2 km of optical fiber. The protocol uses discrete signaling and post-selection to improve reconciliation speed and quantifies security by means of quantum state tomography. Polarization multiplexing and a frequency translation scheme permit transmission of a continuous wave local oscillator and suppression of noise from guided acoustic wave Brillouin scattering by more than 27 dB.

© 2009 Optical Society of America

## 1. Introduction

13. F. Grosshans and P. Grangier, “Reverse reconciliation protocols for quantum cryptography with continuous variables,” http://www.arxiv.org/abs/quant-ph/0204127v1.

17. M. Navascués, F. Grosshans, and A. Acín, “Optimality of Gaussian attacks in continuous-variable quantum cryptography,” Phys. Rev. Lett. **97**, 190502 (2006). [CrossRef] [PubMed]

18. R. Namiki and T. Hirano, “Efficient-phase-encoding protocols for continuous-variable quantum key distribution using coherent states and postselection,” Phys. Rev. A **74**, 032302 (2006). [CrossRef]

22. Z. Zhang and P. L. Voss, “Security of a discretely signaled continuous variable quantum key distribution protocol for high rate systems,” Opt. Exp. **17**, 12090–12108 (2009). [CrossRef]

*I*=

*β I*-max(

_{AB}*χBE*), where

*β*is the efficiency of the error correcting code used in the reconciliation process. For an ideal code that achieves channel capacity,

*β*=1. The quantity

*I*is the classical mutual information for the channel and the signaling scheme between Alice and Bob, and

_{AB}*χ*is the Holevo information between Bob and Eve, which bounds the upper limit of Eve’s accessible information regarding Bob’s measurements. Our recent work [22

_{BE}22. Z. Zhang and P. L. Voss, “Security of a discretely signaled continuous variable quantum key distribution protocol for high rate systems,” Opt. Exp. **17**, 12090–12108 (2009). [CrossRef]

*β*

_{0}, the minimum reconciliation efficiency, which if exceeded, achieves a net positive secret key rate in terms of bits per channel use. In order to lower the efficiency requirement and increase the speed (in bits per second) of the error correcting code that achieves reconciliation, our protocol makes use of discrete signal modulation, reverse reconciliation, post-selection, and quantum state tomography of Bob’s received density matrix to bound Eve’s obtainable information.

7. J. Lodewyck, M. Bloch, R. Garcia-Patron, S. Fossier, E. Karpov, E. Diamanti, T. Debuisschert, N. J. Cerf, R. Tualle-Brouri, S. W. McLaughlin, and P. Grangier, “Quantum key distribution over 25 km with an all-fiber continuous-variable system,” Phys. Rev. A **76**, 042305 (2007). [CrossRef]

9. B. Qi, L. L. Huang, L. Qian, and H. K. Lo, “Experimental study on the Gaussian-modulated coherent-state quantum key distribution over standard telecommunication fibers,” Phys. Rev. A **76**, 052323 (2007). [CrossRef]

5. F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, “Quantum key distribution using gaussian-modulated coherent states,” Nature **421**, 238–241 (2003). [CrossRef] [PubMed]

6. S. Lorenz, N. Korolkova, and G. Leuchs, “Continuous-variable quantum key distribution using polarization encoding and post selection,” Appl. Phys. B **79**, 273–277 (2004). [CrossRef]

10. A. M. Lance, T. Symul, V. Sharma, C. Weedbrook, T. C. Ralph, and P. K. Lam, “No-switching quantum key distribution using broadband modulated coherent light,” Phys. Rev. Lett. **95**, 180503 (2005). [CrossRef] [PubMed]

11. T. Symul, D.J. Alton, S. M. Assad, A. M. Lance, C. Weedbrook, T. C. Ralph, and P. K. Lam, “Experimental demonstration of post-selection-based continuous-variable quantum key distribution in the presence of Gaussian noise,” Phys. Rev. A **76**, 030303(R) (2007). [CrossRef]

23. A. J. Poustie, “Guided acoustic-wave Brillouin scattering with optical pulses,” Opt. Lett. **17**, 574–576 (1992). [CrossRef] [PubMed]

22. Z. Zhang and P. L. Voss, “Security of a discretely signaled continuous variable quantum key distribution protocol for high rate systems,” Opt. Exp. **17**, 12090–12108 (2009). [CrossRef]

## 2. The quantized input-quantized output CVQKD protocol

**17**, 12090–12108 (2009). [CrossRef]

18. R. Namiki and T. Hirano, “Efficient-phase-encoding protocols for continuous-variable quantum key distribution using coherent states and postselection,” Phys. Rev. A **74**, 032302 (2006). [CrossRef]

21. Y. Zhao, M. Heid, J. Rigas, and N. Lütkenhaus, “Asymptotic security of binary modulated continuous-variable quantum key distribution under collective attacks,” Phys. Rev. A **79**, 012307 (2009). [CrossRef]

**Step 1**: In each time slot, Alice sends randomly and equiprobably one of four weak coherent states, as represented in Fig. 1(a), where the radius of the circle indicates somewhat arbitrarily the effective radius of quantum fluctuations.

**Step 2:**Each timeslot is randomly assigned by Bob to “data” or “tomography” subsets. For each data time slot, the measurement axis X or Y is randomly chosen by setting local oscillator phase to 0 or to

*π*/2 radians. For each tomography time slot, a random local oscillator phase of 0,

*π*/4, or

*π*/2 is chosen. Bob also chooses a post-selection threshold. Data having absolute value less than this threshold are discarded. Positive valued data is assigned “1”, Negative data is assigned “-1”.

**Step 3:**Bob now reveals which time slots contain tomography and those that contain post-selected data. Alice then reveals which state was sent during those tomography time slots. Using this information, Bob performs conditional quantum tomography for the four conditional density matrices, which permits calculation of an upper bound on the Holevo information for collective attacks. The protocol is aborted if the the Holevo information is too large.

**Step 4:**Bob then reveals the local oscillator phase associated with each post-selected data sample. For each of these samples, Alice projects the transmitted state onto that axis.

**Step 5:**Bob sends checkbits to Alice over a public channel, i.e. reverse reconcilation. Alice corrects her data to agree with Bob.

**Step 6:**Alice and Bob perform privacy amplification to distill the final secure key.

## 3. Experimental setup and calibration process

*ϕ*corresponds to the first root of the Bessel function

*J*

_{0}(

*ϕ*). The result is that the signal light is ideally entirely frequency shifted away from the optical LO freqency, creating sidebands spaced 2 GHz apart. PM1 and PM2 are separate in order to safely limit the RF power per modulator. The LO and signal are combined on a polarization beam splitter (PBS1) then sent down the transmission channel fiber having linear loss of 5.18 dB.

## 4. Results and discussion

*T*=1.059 shot noise units meet the requirements of the error correction code used in reconciliation. Because in principle Eve could replace the communications channel with a GAWBS-free channel, adding a controlled noise-like source, the excess noise is assumed to be under the control of Eve. According to the protocol, conditional tomography for all four states has been performed. The results show that the average excess noise of the quantum channel at the detector is 0.0024 shot noise units, of which 0.0024 is due to GAWBS noise and any remaining imperfections due to the phase estimation, amplitude modulation, and phase modulation are small and difficult to measure. In Fig.3 the raw homodyne tomography histograms are shown for 10

^{5}samples per phase, which show excellent agreement with the expected Gaussian distribution for coherent light with very small excess noise. For each of the four signal states transmitted by Alice, three angles are used for Bob’s tomography.

**17**, 12090–12108 (2009). [CrossRef]

**17**, 12090–12108 (2009). [CrossRef]

^{-7}bits/channel use. We note that unlike previous experiments, this experiment is not constrained by the time required for the error correction code, but by the data rate, which is limited by the 2 MS/s data acquisition and control card (National Instruments PCI-6115). We have not implemented automatic polarization control at the input of Bob’s PBS2, so the system operates well for 7 minutes before the polarization needs to be readjusted. The same experiment operating at a 20 MHz clock rate would leave us with a final key rate of approximately 60 kilobits/s, which compares to the best current rate of 2 kilobits/s for 25 km of fiber [7

7. J. Lodewyck, M. Bloch, R. Garcia-Patron, S. Fossier, E. Karpov, E. Diamanti, T. Debuisschert, N. J. Cerf, R. Tualle-Brouri, S. W. McLaughlin, and P. Grangier, “Quantum key distribution over 25 km with an all-fiber continuous-variable system,” Phys. Rev. A **76**, 042305 (2007). [CrossRef]

## 5. Conclusion

## Acknowledgments

## References and links

1. | C. H. Bennett and G. Grassard, “Quantum cryptography: public key distribution and coin tossing,” in Proceedings of IEEE International Conference on Computers, Systems, and Signal Processing (IEEE, Newyork, 1984), 175–179. |

2. | A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. |

3. | M. A. Nielsen and I. L. Chuang, |

4. | N. J. Cerf, M. Lévy, and G. Van Assche, “Quantum distribution of Gaussian keys using squeezed states,” Phys. Rev. A |

5. | F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, “Quantum key distribution using gaussian-modulated coherent states,” Nature |

6. | S. Lorenz, N. Korolkova, and G. Leuchs, “Continuous-variable quantum key distribution using polarization encoding and post selection,” Appl. Phys. B |

7. | J. Lodewyck, M. Bloch, R. Garcia-Patron, S. Fossier, E. Karpov, E. Diamanti, T. Debuisschert, N. J. Cerf, R. Tualle-Brouri, S. W. McLaughlin, and P. Grangier, “Quantum key distribution over 25 km with an all-fiber continuous-variable system,” Phys. Rev. A |

8. | S. Fossier, E. Diamanti, T. Debuisschert, R. Tualle-Brouri, and P. Grangier, “Field test of a continuous-variable quantum key distribution prototype,” New. J. Phys. |

9. | B. Qi, L. L. Huang, L. Qian, and H. K. Lo, “Experimental study on the Gaussian-modulated coherent-state quantum key distribution over standard telecommunication fibers,” Phys. Rev. A |

10. | A. M. Lance, T. Symul, V. Sharma, C. Weedbrook, T. C. Ralph, and P. K. Lam, “No-switching quantum key distribution using broadband modulated coherent light,” Phys. Rev. Lett. |

11. | T. Symul, D.J. Alton, S. M. Assad, A. M. Lance, C. Weedbrook, T. C. Ralph, and P. K. Lam, “Experimental demonstration of post-selection-based continuous-variable quantum key distribution in the presence of Gaussian noise,” Phys. Rev. A |

12. | S. L. Braunstein and P. Van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. |

13. | F. Grosshans and P. Grangier, “Reverse reconciliation protocols for quantum cryptography with continuous variables,” http://www.arxiv.org/abs/quant-ph/0204127v1. |

14. | F. Grosshans, “Collective attacks and unconditional security in continuous variable quantum key distribution,” Phys. Rev. Lett. |

15. | M. Navascués and A. Acín, “Security bounds for continuous variable quantum key distribution,” Phys. Rev. Lett. |

16. | R. García-Patrón and N. J. Cerf, “Unconditional optimality of gaussian attacks against continuous-variable quantum key distribution,” Phys. Rev. Lett. |

17. | M. Navascués, F. Grosshans, and A. Acín, “Optimality of Gaussian attacks in continuous-variable quantum cryptography,” Phys. Rev. Lett. |

18. | R. Namiki and T. Hirano, “Efficient-phase-encoding protocols for continuous-variable quantum key distribution using coherent states and postselection,” Phys. Rev. A |

19. | M. Heid and N. Lütkenhaus, “Security of coherent-state quantum cryptography in the presence of Gaussian noise,” Phys. Rev. A |

20. | A. Leverrier and P. Grangier, “Unconditional security proof of long-distance continuous-variable quantum key distribution with discrete modulation,” Phys. Rev. Lett. |

21. | Y. Zhao, M. Heid, J. Rigas, and N. Lütkenhaus, “Asymptotic security of binary modulated continuous-variable quantum key distribution under collective attacks,” Phys. Rev. A |

22. | Z. Zhang and P. L. Voss, “Security of a discretely signaled continuous variable quantum key distribution protocol for high rate systems,” Opt. Exp. |

23. | A. J. Poustie, “Guided acoustic-wave Brillouin scattering with optical pulses,” Opt. Lett. |

**OCIS Codes**

(270.5565) Quantum optics : Quantum communications

(270.5568) Quantum optics : Quantum cryptography

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: October 6, 2009

Revised Manuscript: November 22, 2009

Manuscript Accepted: December 14, 2009

Published: December 18, 2009

**Citation**

Quyen Dinh Xuan, Zheshen Zhang, and Paul L. Voss, "A 24 km fiber-based discretely signaled continuous variable quantum key distribution system," Opt. Express **17**, 24244-24249 (2009)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-26-24244

Sort: Year | Journal | Reset

### References

- C. H. Bennett and G. Grassard, "Quantum cryptography: public key distribution and coin tossing," in Proceedings of IEEE International Conference on Computers, Systems, and Signal Processing (IEEE, New York, 1984), 175- 179.
- A. K. Ekert, "Quantum cryptography based on Bell’s theorem," Phys. Rev. Lett. 67, 661-663 (1991). [CrossRef] [PubMed]
- M. A. Nielsen and I. L. Chuang, Quantum computation and quantum information, (Cambridge University Press, UK, 2000).
- N. J. Cerf, M. Levy, and G. Van Assche, "Quantum distribution of Gaussian keys using squeezed states," Phys. Rev. A 63, 052311 (2001). [CrossRef]
- F. Grosshans, G. Van Assche, J. Wenger, R. Brouri, N. J. Cerf, and P. Grangier, "Quantum key distribution using gaussian-modulated coherent states," Nature 421, 238-241 (2003). [CrossRef] [PubMed]
- S. Lorenz, N. Korolkova, and G. Leuchs, "Continuous-variable quantum key distribution using polarization encoding and post selection," Appl. Phys. B 79, 273-277 (2004). [CrossRef]
- J. Lodewyck, M. Bloch, R. Garcia-Patron, S. Fossier, E. Karpov, E. Diamanti, T. Debuisschert, N. J. Cerf, R. Tualle-Brouri, S. W. McLaughlin, and P. Grangier, "Quantum key distribution over 25 km with an all-fiber continuous-variable system," Phys. Rev. A 76, 042305 (2007). [CrossRef]
- S. Fossier, E. Diamanti, T. Debuisschert, R. Tualle-Brouri, and P. Grangier, "Field test of a continuous-variable quantum key distribution prototype," New. J. Phys. 11, 045023 (2009). [CrossRef]
- B. Qi, L. L. Huang, L. Qian, and H. K. Lo, "Experimental study on the Gaussian-modulated coherent-state quantum key distribution over standard telecommunication fibers," Phys. Rev. A 76, 052323 (2007). [CrossRef]
- A. M. Lance, T. Symul, V. Sharma, C. Weedbrook, T. C. Ralph, and P. K. Lam, "No-switching quantum key distribution using broadband modulated coherent light," Phys. Rev. Lett. 95, 180503 (2005). [CrossRef] [PubMed]
- T. Symul, D.J. Alton, S. M. Assad, A. M. Lance, C. Weedbrook, T. C. Ralph, and P. K. Lam, "Experimental demonstration of post-selection-based continuous-variable quantum key distribution in the presence of Gaussian noise," Phys. Rev. A 76, 030303(R) (2007). [CrossRef]
- S. L. Braunstein and P. Van Loock, "Quantum information with continuous variables," Rev. Mod. Phys. 77, 513-577 (2005). [CrossRef]
- F. Grosshans and P. Grangier, "Reverse reconciliation protocols for quantum cryptography with continuous variables," http://www.arxiv.org/abs/quant-ph/0204127v1.
- F. Grosshans, "Collective attacks and unconditional security in continuous variable quantum key distribution," Phys. Rev. Lett. 94, 020504 (2005). [CrossRef] [PubMed]
- M. Navascues and A. Acin, "Security bounds for continuous variable quantum key distribution," Phys. Rev. Lett. 94, 020505 (2005). [CrossRef] [PubMed]
- R. Garcia-Patron and N. J. Cerf, "Unconditional optimality of gaussian attacks against continuous-variable quantum key distribution," Phys. Rev. Lett. 97, 190503 (2006). [CrossRef] [PubMed]
- M. Navascues, F. Grosshans, and A. Acin, "Optimality of Gaussian attacks in continuous-variable quantum cryptography," Phys. Rev. Lett. 97, 190502 (2006). [CrossRef] [PubMed]
- R. Namiki and T. Hirano, "Efficient-phase-encoding protocols for continuous-variable quantum key distribution using coherent states and postselection," Phys. Rev. A 74, 032302 (2006). [CrossRef]
- M. Heid and N. Lutkenhaus, "Security of coherent-state quantum cryptography in the presence of Gaussian noise," Phys. Rev. A 76, 022313 (2007). [CrossRef]
- A. Leverrier and P. Grangier, "Unconditional security proof of long-distance continuous-variable quantum key distribution with discrete modulation," Phys. Rev. Lett. 102, 180504 (2009). [CrossRef] [PubMed]
- Y. Zhao, M. Heid, J. Rigas, and N. Lutkenhaus, "Asymptotic security of binary modulated continuous-variable quantum key distribution under collective attacks," Phys. Rev. A 79, 012307 (2009). [CrossRef]
- Z. Zhang and P. L. Voss, "Security of a discretely signaled continuous variable quantum key distribution protocol for high rate systems," Opt. Exp. 17, 12090-12108 (2009). [CrossRef]
- A. J. Poustie, "Guided acoustic-wave Brillouin scattering with optical pulses," Opt. Lett. 17, 574-576 (1992). [CrossRef] [PubMed]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.