Abstract

Considering a practical continuous variable quantum key distribution(CVQKD) system, synchronization is of significant importance as it is hardly possible to extract secret keys from unsynchronized strings. In this paper, we proposed a high performance frame synchronization method for CVQKD systems which is capable to operate under low signal-to-noise(SNR) ratios and is compatible with random phase shift induced by quantum channel. A practical implementation of this method with low complexity is presented and its performance is analysed. By adjusting the length of synchronization frame, this method can work well with large range of SNR values which paves the way for longer distance CVQKD.

© 2015 Optical Society of America

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References

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  1. A. Ciurana, J. Martínez-Mateo, M. Peev, A. Poppe, N. Walenta, H. Zbinden, and V. Martłn, “Quantum metropolitan optical network based on wavelength division multiplexing,” Opt. Express 22, 1576–1593 (2014).
    [Crossref] [PubMed]
  2. A. Scherer, B. C. Sanders, and W. Tittel, “Long-distance practical quantum key distribution by entanglement swapping,” Opt. Express 19, 3004–3018 (2011).
    [Crossref] [PubMed]
  3. C. H. Bennett, “Quantum cryptography using any two nonorthogonal states,” Phys. Rev. Lett. 68, 3121 (1992).
    [Crossref] [PubMed]
  4. S. Fossier, E. Diamanti, T. Debuisschert, A. Villing, R. Tualle-Brouri, and P. Grangier, “Field test of a continuous-variable quantum key distribution prototype,” New J. Phys. 11, 045023 (2009).
    [Crossref]
  5. A. Leverrier and P. Grangier, “Long distance quantum key distribution with continuous variables,” in Theory of Quantum Computation, Communication, and Cryptography (Springer, 2014), pp. 143–152.
    [Crossref]
  6. P. Jouguet, S. Kunz-Jacques, A. Leverrier, P. Grangier, and E. Diamanti, “Experimental demonstration of long-distance continuous-variable quantum key distribution,” Nat. Photonics 7, 378–381 (2013).
    [Crossref]
  7. W. Dai, Y. Lu, J. Zhu, and G. Zeng, “An integrated quantum secure communication system,” Sci. China Inf. Sci. 54, 2578–2591 (2011).
    [Crossref]
  8. Z. Shen, J. Fang, G. He, and G. Zeng, “Synchronous scheme and experimental realization in continuous variable quantum key distribution system,” Chinese J. Laser 40, 130–135 (2013).
  9. Y. Liu, C. Wang, D. Huang, P. Huang, X. Feng, J. Peng, Z. Cao, and G. Zeng, “Study of synchronous technology in high-speed continuous variable quantum key distribution system,” Acta Optica Sinica 35, 96–105 (2015).
  10. D. North, “An analysis of the factors which determine signal/noise discrimination in pulsed-carrier systems,” in Proceedings of the IEEE (IEEE, 1963), pp. 1016–1027.
    [Crossref]
  11. P. Jouguet, S. Kunz-Jacques, and E. Diamanti, “Preventing calibration attacks on the local oscillator in continuous-variable quantum key distribution,” Phys. Rev. A 87, 062313 (2013).
    [Crossref]
  12. P. Huang, J. Fang, and G. Zeng, “State-discrimination attack on discretely modulated continuous-variable quantum key distribution,” Phys. Rev. A 89, 042330 (2014).
    [Crossref]

2015 (1)

Y. Liu, C. Wang, D. Huang, P. Huang, X. Feng, J. Peng, Z. Cao, and G. Zeng, “Study of synchronous technology in high-speed continuous variable quantum key distribution system,” Acta Optica Sinica 35, 96–105 (2015).

2014 (2)

A. Ciurana, J. Martínez-Mateo, M. Peev, A. Poppe, N. Walenta, H. Zbinden, and V. Martłn, “Quantum metropolitan optical network based on wavelength division multiplexing,” Opt. Express 22, 1576–1593 (2014).
[Crossref] [PubMed]

P. Huang, J. Fang, and G. Zeng, “State-discrimination attack on discretely modulated continuous-variable quantum key distribution,” Phys. Rev. A 89, 042330 (2014).
[Crossref]

2013 (3)

P. Jouguet, S. Kunz-Jacques, A. Leverrier, P. Grangier, and E. Diamanti, “Experimental demonstration of long-distance continuous-variable quantum key distribution,” Nat. Photonics 7, 378–381 (2013).
[Crossref]

P. Jouguet, S. Kunz-Jacques, and E. Diamanti, “Preventing calibration attacks on the local oscillator in continuous-variable quantum key distribution,” Phys. Rev. A 87, 062313 (2013).
[Crossref]

Z. Shen, J. Fang, G. He, and G. Zeng, “Synchronous scheme and experimental realization in continuous variable quantum key distribution system,” Chinese J. Laser 40, 130–135 (2013).

2011 (2)

W. Dai, Y. Lu, J. Zhu, and G. Zeng, “An integrated quantum secure communication system,” Sci. China Inf. Sci. 54, 2578–2591 (2011).
[Crossref]

A. Scherer, B. C. Sanders, and W. Tittel, “Long-distance practical quantum key distribution by entanglement swapping,” Opt. Express 19, 3004–3018 (2011).
[Crossref] [PubMed]

2009 (1)

S. Fossier, E. Diamanti, T. Debuisschert, A. Villing, R. Tualle-Brouri, and P. Grangier, “Field test of a continuous-variable quantum key distribution prototype,” New J. Phys. 11, 045023 (2009).
[Crossref]

1992 (1)

C. H. Bennett, “Quantum cryptography using any two nonorthogonal states,” Phys. Rev. Lett. 68, 3121 (1992).
[Crossref] [PubMed]

Bennett, C. H.

C. H. Bennett, “Quantum cryptography using any two nonorthogonal states,” Phys. Rev. Lett. 68, 3121 (1992).
[Crossref] [PubMed]

Cao, Z.

Y. Liu, C. Wang, D. Huang, P. Huang, X. Feng, J. Peng, Z. Cao, and G. Zeng, “Study of synchronous technology in high-speed continuous variable quantum key distribution system,” Acta Optica Sinica 35, 96–105 (2015).

Ciurana, A.

Dai, W.

W. Dai, Y. Lu, J. Zhu, and G. Zeng, “An integrated quantum secure communication system,” Sci. China Inf. Sci. 54, 2578–2591 (2011).
[Crossref]

Debuisschert, T.

S. Fossier, E. Diamanti, T. Debuisschert, A. Villing, R. Tualle-Brouri, and P. Grangier, “Field test of a continuous-variable quantum key distribution prototype,” New J. Phys. 11, 045023 (2009).
[Crossref]

Diamanti, E.

P. Jouguet, S. Kunz-Jacques, A. Leverrier, P. Grangier, and E. Diamanti, “Experimental demonstration of long-distance continuous-variable quantum key distribution,” Nat. Photonics 7, 378–381 (2013).
[Crossref]

P. Jouguet, S. Kunz-Jacques, and E. Diamanti, “Preventing calibration attacks on the local oscillator in continuous-variable quantum key distribution,” Phys. Rev. A 87, 062313 (2013).
[Crossref]

S. Fossier, E. Diamanti, T. Debuisschert, A. Villing, R. Tualle-Brouri, and P. Grangier, “Field test of a continuous-variable quantum key distribution prototype,” New J. Phys. 11, 045023 (2009).
[Crossref]

Fang, J.

P. Huang, J. Fang, and G. Zeng, “State-discrimination attack on discretely modulated continuous-variable quantum key distribution,” Phys. Rev. A 89, 042330 (2014).
[Crossref]

Z. Shen, J. Fang, G. He, and G. Zeng, “Synchronous scheme and experimental realization in continuous variable quantum key distribution system,” Chinese J. Laser 40, 130–135 (2013).

Feng, X.

Y. Liu, C. Wang, D. Huang, P. Huang, X. Feng, J. Peng, Z. Cao, and G. Zeng, “Study of synchronous technology in high-speed continuous variable quantum key distribution system,” Acta Optica Sinica 35, 96–105 (2015).

Fossier, S.

S. Fossier, E. Diamanti, T. Debuisschert, A. Villing, R. Tualle-Brouri, and P. Grangier, “Field test of a continuous-variable quantum key distribution prototype,” New J. Phys. 11, 045023 (2009).
[Crossref]

Grangier, P.

P. Jouguet, S. Kunz-Jacques, A. Leverrier, P. Grangier, and E. Diamanti, “Experimental demonstration of long-distance continuous-variable quantum key distribution,” Nat. Photonics 7, 378–381 (2013).
[Crossref]

S. Fossier, E. Diamanti, T. Debuisschert, A. Villing, 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, “Long distance quantum key distribution with continuous variables,” in Theory of Quantum Computation, Communication, and Cryptography (Springer, 2014), pp. 143–152.
[Crossref]

He, G.

Z. Shen, J. Fang, G. He, and G. Zeng, “Synchronous scheme and experimental realization in continuous variable quantum key distribution system,” Chinese J. Laser 40, 130–135 (2013).

Huang, D.

Y. Liu, C. Wang, D. Huang, P. Huang, X. Feng, J. Peng, Z. Cao, and G. Zeng, “Study of synchronous technology in high-speed continuous variable quantum key distribution system,” Acta Optica Sinica 35, 96–105 (2015).

Huang, P.

Y. Liu, C. Wang, D. Huang, P. Huang, X. Feng, J. Peng, Z. Cao, and G. Zeng, “Study of synchronous technology in high-speed continuous variable quantum key distribution system,” Acta Optica Sinica 35, 96–105 (2015).

P. Huang, J. Fang, and G. Zeng, “State-discrimination attack on discretely modulated continuous-variable quantum key distribution,” Phys. Rev. A 89, 042330 (2014).
[Crossref]

Jouguet, P.

P. Jouguet, S. Kunz-Jacques, and E. Diamanti, “Preventing calibration attacks on the local oscillator in continuous-variable quantum key distribution,” Phys. Rev. A 87, 062313 (2013).
[Crossref]

P. Jouguet, S. Kunz-Jacques, A. Leverrier, P. Grangier, and E. Diamanti, “Experimental demonstration of long-distance continuous-variable quantum key distribution,” Nat. Photonics 7, 378–381 (2013).
[Crossref]

Kunz-Jacques, S.

P. Jouguet, S. Kunz-Jacques, A. Leverrier, P. Grangier, and E. Diamanti, “Experimental demonstration of long-distance continuous-variable quantum key distribution,” Nat. Photonics 7, 378–381 (2013).
[Crossref]

P. Jouguet, S. Kunz-Jacques, and E. Diamanti, “Preventing calibration attacks on the local oscillator in continuous-variable quantum key distribution,” Phys. Rev. A 87, 062313 (2013).
[Crossref]

Leverrier, A.

P. Jouguet, S. Kunz-Jacques, A. Leverrier, P. Grangier, and E. Diamanti, “Experimental demonstration of long-distance continuous-variable quantum key distribution,” Nat. Photonics 7, 378–381 (2013).
[Crossref]

A. Leverrier and P. Grangier, “Long distance quantum key distribution with continuous variables,” in Theory of Quantum Computation, Communication, and Cryptography (Springer, 2014), pp. 143–152.
[Crossref]

Liu, Y.

Y. Liu, C. Wang, D. Huang, P. Huang, X. Feng, J. Peng, Z. Cao, and G. Zeng, “Study of synchronous technology in high-speed continuous variable quantum key distribution system,” Acta Optica Sinica 35, 96–105 (2015).

Lu, Y.

W. Dai, Y. Lu, J. Zhu, and G. Zeng, “An integrated quantum secure communication system,” Sci. China Inf. Sci. 54, 2578–2591 (2011).
[Crossref]

Martínez-Mateo, J.

Martln, V.

North, D.

D. North, “An analysis of the factors which determine signal/noise discrimination in pulsed-carrier systems,” in Proceedings of the IEEE (IEEE, 1963), pp. 1016–1027.
[Crossref]

Peev, M.

Peng, J.

Y. Liu, C. Wang, D. Huang, P. Huang, X. Feng, J. Peng, Z. Cao, and G. Zeng, “Study of synchronous technology in high-speed continuous variable quantum key distribution system,” Acta Optica Sinica 35, 96–105 (2015).

Poppe, A.

Sanders, B. C.

Scherer, A.

Shen, Z.

Z. Shen, J. Fang, G. He, and G. Zeng, “Synchronous scheme and experimental realization in continuous variable quantum key distribution system,” Chinese J. Laser 40, 130–135 (2013).

Tittel, W.

Tualle-Brouri, R.

S. Fossier, E. Diamanti, T. Debuisschert, A. Villing, R. Tualle-Brouri, and P. Grangier, “Field test of a continuous-variable quantum key distribution prototype,” New J. Phys. 11, 045023 (2009).
[Crossref]

Villing, A.

S. Fossier, E. Diamanti, T. Debuisschert, A. Villing, R. Tualle-Brouri, and P. Grangier, “Field test of a continuous-variable quantum key distribution prototype,” New J. Phys. 11, 045023 (2009).
[Crossref]

Walenta, N.

Wang, C.

Y. Liu, C. Wang, D. Huang, P. Huang, X. Feng, J. Peng, Z. Cao, and G. Zeng, “Study of synchronous technology in high-speed continuous variable quantum key distribution system,” Acta Optica Sinica 35, 96–105 (2015).

Zbinden, H.

Zeng, G.

Y. Liu, C. Wang, D. Huang, P. Huang, X. Feng, J. Peng, Z. Cao, and G. Zeng, “Study of synchronous technology in high-speed continuous variable quantum key distribution system,” Acta Optica Sinica 35, 96–105 (2015).

P. Huang, J. Fang, and G. Zeng, “State-discrimination attack on discretely modulated continuous-variable quantum key distribution,” Phys. Rev. A 89, 042330 (2014).
[Crossref]

Z. Shen, J. Fang, G. He, and G. Zeng, “Synchronous scheme and experimental realization in continuous variable quantum key distribution system,” Chinese J. Laser 40, 130–135 (2013).

W. Dai, Y. Lu, J. Zhu, and G. Zeng, “An integrated quantum secure communication system,” Sci. China Inf. Sci. 54, 2578–2591 (2011).
[Crossref]

Zhu, J.

W. Dai, Y. Lu, J. Zhu, and G. Zeng, “An integrated quantum secure communication system,” Sci. China Inf. Sci. 54, 2578–2591 (2011).
[Crossref]

Acta Optica Sinica (1)

Y. Liu, C. Wang, D. Huang, P. Huang, X. Feng, J. Peng, Z. Cao, and G. Zeng, “Study of synchronous technology in high-speed continuous variable quantum key distribution system,” Acta Optica Sinica 35, 96–105 (2015).

Chinese J. Laser (1)

Z. Shen, J. Fang, G. He, and G. Zeng, “Synchronous scheme and experimental realization in continuous variable quantum key distribution system,” Chinese J. Laser 40, 130–135 (2013).

Nat. Photonics (1)

P. Jouguet, S. Kunz-Jacques, A. Leverrier, P. Grangier, and E. Diamanti, “Experimental demonstration of long-distance continuous-variable quantum key distribution,” Nat. Photonics 7, 378–381 (2013).
[Crossref]

New J. Phys. (1)

S. Fossier, E. Diamanti, T. Debuisschert, A. Villing, R. Tualle-Brouri, and P. Grangier, “Field test of a continuous-variable quantum key distribution prototype,” New J. Phys. 11, 045023 (2009).
[Crossref]

Opt. Express (2)

Phys. Rev. A (2)

P. Jouguet, S. Kunz-Jacques, and E. Diamanti, “Preventing calibration attacks on the local oscillator in continuous-variable quantum key distribution,” Phys. Rev. A 87, 062313 (2013).
[Crossref]

P. Huang, J. Fang, and G. Zeng, “State-discrimination attack on discretely modulated continuous-variable quantum key distribution,” Phys. Rev. A 89, 042330 (2014).
[Crossref]

Phys. Rev. Lett. (1)

C. H. Bennett, “Quantum cryptography using any two nonorthogonal states,” Phys. Rev. Lett. 68, 3121 (1992).
[Crossref] [PubMed]

Sci. China Inf. Sci. (1)

W. Dai, Y. Lu, J. Zhu, and G. Zeng, “An integrated quantum secure communication system,” Sci. China Inf. Sci. 54, 2578–2591 (2011).
[Crossref]

Other (2)

D. North, “An analysis of the factors which determine signal/noise discrimination in pulsed-carrier systems,” in Proceedings of the IEEE (IEEE, 1963), pp. 1016–1027.
[Crossref]

A. Leverrier and P. Grangier, “Long distance quantum key distribution with continuous variables,” in Theory of Quantum Computation, Communication, and Cryptography (Springer, 2014), pp. 143–152.
[Crossref]

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Figures (4)

Fig. 1
Fig. 1 Demonstration of correlation peak. Figure 1 shows the self-correlation result of synchronization signal S, i.e. cov(S, S), and Fig. 2 shows the correlation result of cov(S, Y) with SNR = −6 dB.
Fig. 2
Fig. 2 Realization of synchronization scheme
Fig. 3
Fig. 3 Synchronization success rate for SNR from −10dB to −20dB. From the bottom to the top we used the following length of S: 1024, 2048, 4096, 8192. The solid curves are the theoretical performance line according to section 3.1, the dash lines with triangle markers are practical performance without quantization and the dash lines with square markers are practical performance with S quantized to 9 levels.
Fig. 4
Fig. 4 Synchronization success rate for Δφ from 0° to 180°. The corresponding length of S from the bottom to the top is: 512,1024,2048.

Equations (21)

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{ R i = max ( S ) P i = cos 1 ( S i max ( S ) ) , i = 1 , 2 , , L .
cov ( S , S ^ ) = E { R cos ( P ) R cos ( P + Δ φ ) } = E { R 2 } E { cos ( P ) cos ( P + Δ φ ) } cos ( Δ φ ) V A ,
S ^ i = R i cos ( P i Δ θ i + Δ φ ) = R i cos ( P i + δ θ ) .
P Z ( u ) = P X Y ( u ) = K 0 ( | u | σ X σ Y ) π σ X σ Y ,
E ( Z ) = 1 π σ Z σ Y u K 0 ( | u | σ X σ Y ) d u ,
cov ( S , N ) ~ N ( 0 , V A V N L ) .
cov ( S , S ) = L E { S S } = L E { R 2 } E { cos 2 ( P ) } = V A L ,
cov ( S , S ^ ) = cov ( S , S ) + cov ( S , N ) ~ N ( V A L , V A V N L ) .
cov ( S , Y ) = cov ( S , X ) + cov ( S , N ) ~ N ( 0 , ( V A 2 + V A V N ) L ) .
P suc = P ( cov ( S , S ^ ) > max ( cov ( S , Y ) ) )
= P ( x > 0 | x ~ N ( μ 1 , σ 1 2 ) ) ,
μ 1 = V A L 3 V A ( V A + V N ) L ,
σ 1 = V A V N L ,
cov ( S L , S ^ L ) = cov ( S L / 2 , S ^ L / 2 ) + cov ( S L / 2 , Y L / 2 )
= cov ( S L / 2 , S L / 2 ) + cov ( S L / 2 , N L / 2 ) + cov ( S L / 2 , Y L / 2 )
~ N ( 1 2 V A L , V A ( 3 V A + 4 V N ) L 2 ) ,
P ¨ suc = P ( cov ( S L , S ^ L ) > max ( cov ( S L , Y L ) ) )
= P ( x > 0 | x ~ N ( μ 2 , σ 2 2 ) ) ,
μ 2 = 1 2 V A L 3 V A ( V A + V N ) L ,
σ 2 = V A ( 3 V A + 4 V N ) L 2 ) .
{ R i = S i 2 + G i 2 P i = cos 1 ( S i S i 2 + G i 2 ) , i = 1 , 2 , , L .

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