## 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

Full Article | PDF Article**OSA Recommended Articles**

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### References

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- 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.

- 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. Lévy, 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. Navascués and A. Acín, “Security bounds for continuous variable quantum key distribution,” Phys. Rev. Lett. 94, 020505 (2005).

[Crossref] [PubMed] - R. García-Patrón and N. J. Cerf, “Unconditional optimality of gaussian attacks against continuous-variable quantum key distribution,” Phys. Rev. Lett. 97, 190503 (2006).

[Crossref] [PubMed] - M. Navascués, F. Grosshans, and A. Acín, “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. Lütkenhaus, “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. Lütkenhaus, “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]

#### 2009 (4)

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]

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. Lütkenhaus, “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]

#### 2007 (4)

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]

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]

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]

M. Heid and N. Lütkenhaus, “Security of coherent-state quantum cryptography in the presence of Gaussian noise,” Phys. Rev. A 76, 022313 (2007).

[Crossref]

#### 2006 (3)

R. García-Patrón and N. J. Cerf, “Unconditional optimality of gaussian attacks against continuous-variable quantum key distribution,” Phys. Rev. Lett. 97, 190503 (2006).

[Crossref]
[PubMed]

M. Navascués, F. Grosshans, and A. Acín, “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]

#### 2005 (4)

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]

S. L. Braunstein and P. Van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77, 513–577 (2005).

[Crossref]

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

[Crossref]
[PubMed]

M. Navascués and A. Acín, “Security bounds for continuous variable quantum key distribution,” Phys. Rev. Lett. 94, 020505 (2005).

[Crossref]
[PubMed]

#### 2004 (1)

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]

#### 2003 (1)

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]

#### 2001 (1)

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

[Crossref]

#### 1992 (1)

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

[Crossref]
[PubMed]

#### 1991 (1)

A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67, 661–663 (1991).

[Crossref]
[PubMed]

#### 1984 (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.

#### Acín, A.

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

[Crossref]
[PubMed]

M. Navascués and A. Acín, “Security bounds for continuous variable quantum key distribution,” Phys. Rev. Lett. 94, 020505 (2005).

[Crossref]
[PubMed]

#### Alton, D.J.

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]

#### Assad, S. M.

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]

#### Bennett, C. H.

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.

#### Bloch, M.

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]

#### Braunstein, S. L.

S. L. Braunstein and P. Van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77, 513–577 (2005).

[Crossref]

#### Brouri, R.

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]

#### Cerf, N. J.

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]

R. García-Patrón and N. J. Cerf, “Unconditional optimality of gaussian attacks against continuous-variable quantum key distribution,” Phys. Rev. Lett. 97, 190503 (2006).

[Crossref]
[PubMed]

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]

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

[Crossref]

#### Chuang, I. L.

M. A. Nielsen and I. L. Chuang, Quantum computation and quantum information, (Cambridge University Press, UK, 2000).

#### Debuisschert, T.

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]

[Crossref]

#### Diamanti, E.

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]

[Crossref]

#### Ekert, A. K.

A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67, 661–663 (1991).

[Crossref]
[PubMed]

#### Fossier, S.

[Crossref]

[Crossref]

#### Garcia-Patron, R.

[Crossref]

#### García-Patrón, R.

R. García-Patrón and N. J. Cerf, “Unconditional optimality of gaussian attacks against continuous-variable quantum key distribution,” Phys. Rev. Lett. 97, 190503 (2006).

[Crossref]
[PubMed]

#### Grangier, P.

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]

[Crossref]

[Crossref]

[Crossref]
[PubMed]

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

#### Grassard, G.

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.

#### Grosshans, F.

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

[Crossref]
[PubMed]

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

[Crossref]
[PubMed]

[Crossref]
[PubMed]

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

#### Heid, M.

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]

M. Heid and N. Lütkenhaus, “Security of coherent-state quantum cryptography in the presence of Gaussian noise,” Phys. Rev. A 76, 022313 (2007).

[Crossref]

#### Hirano, T.

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]

#### Huang, L. L.

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]

#### Karpov, E.

[Crossref]

#### Korolkova, N.

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]

#### Lam, P. K.

[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]

#### Lance, A. M.

[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]

#### Leuchs, G.

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]

#### Leverrier, A.

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]

#### Lévy, M.

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

[Crossref]

#### Lo, H. K.

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]

#### Lodewyck, J.

[Crossref]

#### Lorenz, S.

[Crossref]

#### Lütkenhaus, N.

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]

M. Heid and N. Lütkenhaus, “Security of coherent-state quantum cryptography in the presence of Gaussian noise,” Phys. Rev. A 76, 022313 (2007).

[Crossref]

#### McLaughlin, S. W.

[Crossref]

#### Namiki, R.

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]

#### Navascués, M.

[Crossref]
[PubMed]

M. Navascués and A. Acín, “Security bounds for continuous variable quantum key distribution,” Phys. Rev. Lett. 94, 020505 (2005).

[Crossref]
[PubMed]

#### Nielsen, M. A.

M. A. Nielsen and I. L. Chuang, Quantum computation and quantum information, (Cambridge University Press, UK, 2000).

#### Poustie, A. J.

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

[Crossref]
[PubMed]

#### Qi, B.

[Crossref]

#### Qian, L.

[Crossref]

#### Ralph, T. C.

[Crossref]

[Crossref]
[PubMed]

#### Rigas, J.

[Crossref]

#### Sharma, V.

[Crossref]
[PubMed]

#### Symul, T.

[Crossref]

[Crossref]
[PubMed]

#### Tualle-Brouri, R.

[Crossref]

[Crossref]

#### Van Assche, G.

[Crossref]
[PubMed]

[Crossref]

#### Van Loock, P.

S. L. Braunstein and P. Van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77, 513–577 (2005).

[Crossref]

#### Voss, P. L.

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]

#### Weedbrook, C.

[Crossref]

[Crossref]
[PubMed]

#### Wenger, J.

[Crossref]
[PubMed]

#### Zhang, Z.

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]

#### Zhao, Y.

[Crossref]

#### Appl. Phys. B (1)

[Crossref]

#### Nature (1)

[Crossref]
[PubMed]

#### New. J. Phys. (1)

[Crossref]

#### Opt. Exp. (1)

[Crossref]

#### Opt. Lett. (1)

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

[Crossref]
[PubMed]

#### Phys. Rev. A (7)

[Crossref]

[Crossref]

[Crossref]

[Crossref]

[Crossref]

[Crossref]

[Crossref]

#### Phys. Rev. Lett. (7)

[Crossref]
[PubMed]

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

[Crossref]
[PubMed]

[Crossref]
[PubMed]

[Crossref]
[PubMed]

[Crossref]
[PubMed]

A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67, 661–663 (1991).

[Crossref]
[PubMed]

[Crossref]
[PubMed]

#### Rev. Mod. Phys. (1)

[Crossref]

#### Other (3)

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

M. A. Nielsen and I. L. Chuang, Quantum computation and quantum information, (Cambridge University Press, UK, 2000).

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### Figures (3)

**Fig. 1.**

Conceptual schematic for (a) quadrature phase-shift keyed (QPSK) signaling, with |αi〉 chosen equiprobably and (b) effect of channel, where _{B}
_{1}〉) denotes Bob’s received quantum state conditioned on Alice sending |_{1}〉. Channel loss causes an attenuation of signal amplitude. The increase in diameter indicates schematically noise that is potentially added by Eve or the channel. (c-top) Final LO spectrum before homodyne detection. (c-bottom) Final signal spectrum before homodyne detection.

**Fig. 2.**

Schematic of experiment, with abbreviations defined in text.

**Fig. 3.**

Tomography data with Gaussian fit