Abstract

We address feasibility of continuous-variable quantum key distribution using bright multimode coherent states of light and homodyne detection. We experimentally verify the possibility to properly select signal modes by matching them with the local oscillator and this way to decrease the quadrature noise concerned with unmatched bright modes. We apply the results to theoretically predict the performance of continuous-variable quantum key distribution scheme using multimode coherent states in scenarios where modulation is applied either to all the modes or only to the matched ones, and confirm that the protocol is feasible at high overall brightness. Our results open the pathway towards full-scale implementation of quantum key distribution using bright light, thus bringing quantum communication closer to classical optics.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
  3. E. Diamanti, H.-K. Lo, B. Qi, and Z. Yuan, “Practical challenges in quantum key distribution,” npj Quantum Inf. 2(1), 16025 (2016).
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  4. S. Pirandola, U. L. Andersen, L. Banchi, M. Berta, D. Bunandar, R. Colbeck, D. Englund, T. Gehring, C. Lupo, C. Ottaviani, J. Pereira, M. Razavi, J. S. Shaari, M. Tomamichel, V. C. Usenko, G. Vallone, P. Villoresi, and P. Wallden, “Advances in quantum cryptography,” arXiv:1906.01645[quant-ph] (2019).
  5. C. H. Bennett and G. Brassard, “Quantum cryptography: public key distribution and coin tossing,” Proceedings of International Conference on Computers, Systems and Signal Processing (IEEE, 1984), pp. 175–179.
  6. H.-K. Lo, X. Ma, and K. Chen, “Decoy state quantum key distribution,” Phys. Rev. Lett. 94(23), 230504 (2005).
    [Crossref]
  7. T. C. Ralph, “Continuous variable quantum cryptography,” Phys. Rev. A 61(1), 010303 (1999).
    [Crossref]
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  9. C. Weedbrook, A. M. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam, “Quantum cryptography without switching,” Phys. Rev. Lett. 93(17), 170504 (2004).
    [Crossref]
  10. V. C. Usenko and F. Grosshans, “Unidimensional continuous-variable quantum key distribution,” Phys. Rev. A 92(6), 062337 (2015).
    [Crossref]
  11. R. García-Patrón and N. J. Cerf, “Continuous-variable quantum key distribution protocols over noisy channels,” Phys. Rev. Lett. 102(13), 130501 (2009).
    [Crossref]
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    [Crossref]
  13. L. S. Madsen, V. C. Usenko, M. Lassen, R. Filip, and U. L. Andersen, “Continuous variable quantum key distribution with modulated entangled states,” Nat. Commun. 3(1), 1083 (2012).
    [Crossref]
  14. M. Lasota, R. Filip, and V. C. Usenko, “Robustness of quantum key distribution with discrete and continuous variables to channel noise,” Phys. Rev. A 95(6), 062312 (2017).
    [Crossref]
  15. V. C. Usenko, L. Ruppert, and R. Filip, “Entanglement-based continuous-variable quantum key distribution with multimode states and detectors,” Phys. Rev. A 90(6), 062326 (2014).
    [Crossref]
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    [Crossref]
  17. D. B. S. Soh, C. Brif, P. J. Coles, N. Lütkenhaus, R. M. Camacho, J. Urayama, and M. Sarovar, “Self-referenced continuous-variable quantum key distribution protocol,” Phys. Rev. X 5(4), 041010 (2015).
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    [Crossref]
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    [Crossref]
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    [Crossref]
  22. 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(5), 378–381 (2013).
    [Crossref]
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    [Crossref]
  24. D. Huang, P. Huang, D. Lin, and G. Zeng, “Long-distance continuous-variable quantum key distribution by controlling excess noise,” Sci. Rep. 6(1), 19201 (2016).
    [Crossref]
  25. I. Derkach, V. C. Usenko, and R. Filip, “Preventing side-channel effects in continuous-variable quantum key distribution,” Phys. Rev. A 93(3), 032309 (2016).
    [Crossref]
  26. T. Iskhakov, M. V. Chekhova, and G. Leuchs, “Generation and direct detection of broadband mesoscopic polarization-squeezed vacuum,” Phys. Rev. Lett. 102(18), 183602 (2009).
    [Crossref]
  27. A. Leverrier, R. García-Patrón, R. Renner, and N. J. Cerf, “Security of continuous-variable quantum key distribution against general attacks,” Phys. Rev. Lett. 110(3), 030502 (2013).
    [Crossref]
  28. A. Leverrier, F. Grosshans, and P. Grangier, “Finite-size analysis of a continuous-variable quantum key distribution,” Phys. Rev. A 81(6), 062343 (2010).
    [Crossref]
  29. A. Leverrier, “Security of continuous-variable quantum key distribution via a gaussian de finetti reduction,” Phys. Rev. Lett. 118(20), 200501 (2017).
    [Crossref]
  30. C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84(2), 621–669 (2012).
    [Crossref]
  31. V. C. Usenko and R. Filip, “Trusted noise in continuous-variable quantum key distribution: A threat and a defense,” Entropy 18(1), 20 (2016).
    [Crossref]
  32. I. Derkach, V. C. Usenko, and R. Filip, “Continuous-variable quantum key distribution with a leakage from state preparation,” Phys. Rev. A 96(6), 062309 (2017).
    [Crossref]
  33. V. C. Usenko, B. Heim, C. Peuntinger, C. Wittmann, C. Marquardt, G. Leuchs, and R. Filip, “Entanglement of gaussian states and the applicability to quantum key distribution over fading channels,” New J. Phys. 14(9), 093048 (2012).
    [Crossref]
  34. D. Vasylyev, A. A. Semenov, W. Vogel, K. Günthner, A. Thurn, O. Bayraktar, and C. Marquardt, “Free-space quantum links under diverse weather conditions,” Phys. Rev. A 96(4), 043856 (2017).
    [Crossref]
  35. I. Derkach, V. C. Usenko, and R. Filip, “Squeezing-enhanced quantum key distribution over atmospheric channels,” arXiv:1809.10167 [quant-ph] (2018).
  36. P. Jouguet, S. Kunz-Jacques, and A. Leverrier, “Long-distance continuous-variable quantum key distribution with a gaussian modulation,” Phys. Rev. A 84(6), 062317 (2011).
    [Crossref]
  37. Y. Shaked, Y. Michael, R. Z. Vered, L. Bello, M. Rosenbluh, and A. Pe’er, “Lifting the bandwidth limit of optical homodyne measurement with broadband parametric amplification,” Nat. Commun. 9(1), 609 (2018).
    [Crossref]
  38. T. A. Eriksson, T. Hirano, B. J. Puttnam, G. Rademacher, R. S. Luís, M. Fujiwara, R. Namiki, Y. Awaji, M. Takeoka, N. Wada, and M. Sasaki, “Wavelength division multiplexing of continuous variable quantum key distribution and 18.3 tbit/s data channels,” Commun. Phys. 2(1), 9 (2019).
    [Crossref]
  39. G. Ferrini, J. P. Gazeau, T. Coudreau, C. Fabre, and N. Treps, “Compact gaussian quantum computation by multi-pixel homodyne detection,” New J. Phys. 15(9), 093015 (2013).
    [Crossref]

2019 (1)

T. A. Eriksson, T. Hirano, B. J. Puttnam, G. Rademacher, R. S. Luís, M. Fujiwara, R. Namiki, Y. Awaji, M. Takeoka, N. Wada, and M. Sasaki, “Wavelength division multiplexing of continuous variable quantum key distribution and 18.3 tbit/s data channels,” Commun. Phys. 2(1), 9 (2019).
[Crossref]

2018 (1)

Y. Shaked, Y. Michael, R. Z. Vered, L. Bello, M. Rosenbluh, and A. Pe’er, “Lifting the bandwidth limit of optical homodyne measurement with broadband parametric amplification,” Nat. Commun. 9(1), 609 (2018).
[Crossref]

2017 (4)

D. Vasylyev, A. A. Semenov, W. Vogel, K. Günthner, A. Thurn, O. Bayraktar, and C. Marquardt, “Free-space quantum links under diverse weather conditions,” Phys. Rev. A 96(4), 043856 (2017).
[Crossref]

A. Leverrier, “Security of continuous-variable quantum key distribution via a gaussian de finetti reduction,” Phys. Rev. Lett. 118(20), 200501 (2017).
[Crossref]

I. Derkach, V. C. Usenko, and R. Filip, “Continuous-variable quantum key distribution with a leakage from state preparation,” Phys. Rev. A 96(6), 062309 (2017).
[Crossref]

M. Lasota, R. Filip, and V. C. Usenko, “Robustness of quantum key distribution with discrete and continuous variables to channel noise,” Phys. Rev. A 95(6), 062312 (2017).
[Crossref]

2016 (4)

D. Huang, P. Huang, D. Lin, and G. Zeng, “Long-distance continuous-variable quantum key distribution by controlling excess noise,” Sci. Rep. 6(1), 19201 (2016).
[Crossref]

I. Derkach, V. C. Usenko, and R. Filip, “Preventing side-channel effects in continuous-variable quantum key distribution,” Phys. Rev. A 93(3), 032309 (2016).
[Crossref]

E. Diamanti, H.-K. Lo, B. Qi, and Z. Yuan, “Practical challenges in quantum key distribution,” npj Quantum Inf. 2(1), 16025 (2016).
[Crossref]

V. C. Usenko and R. Filip, “Trusted noise in continuous-variable quantum key distribution: A threat and a defense,” Entropy 18(1), 20 (2016).
[Crossref]

2015 (6)

D. B. S. Soh, C. Brif, P. J. Coles, N. Lütkenhaus, R. M. Camacho, J. Urayama, and M. Sarovar, “Self-referenced continuous-variable quantum key distribution protocol,” Phys. Rev. X 5(4), 041010 (2015).
[Crossref]

B. Qi, P. Lougovski, R. Pooser, W. Grice, and M. Bobrek, “Generating the local oscillator “locally” in continuous-variable quantum key distribution based on coherent detection,” Phys. Rev. X 5(4), 041009 (2015).
[Crossref]

D. Huang, D. Lin, C. Wang, W. Liu, S. Fang, J. Peng, P. Huang, and G. Zeng, “Continuous-variable quantum key distribution with 1 mbps secure key rate,” Opt. Express 23(13), 17511–17519 (2015).
[Crossref]

D. Huang, P. Huang, D. Lin, C. Wang, and G. Zeng, “High-speed continuous-variable quantum key distribution without sending a local oscillator,” Opt. Lett. 40(16), 3695–3698 (2015).
[Crossref]

V. C. Usenko, L. Ruppert, and R. Filip, “Quantum communication with macroscopically bright nonclassical states,” Opt. Express 23(24), 31534–31543 (2015).
[Crossref]

V. C. Usenko and F. Grosshans, “Unidimensional continuous-variable quantum key distribution,” Phys. Rev. A 92(6), 062337 (2015).
[Crossref]

2014 (1)

V. C. Usenko, L. Ruppert, and R. Filip, “Entanglement-based continuous-variable quantum key distribution with multimode states and detectors,” Phys. Rev. A 90(6), 062326 (2014).
[Crossref]

2013 (3)

A. Leverrier, R. García-Patrón, R. Renner, and N. J. Cerf, “Security of continuous-variable quantum key distribution against general attacks,” Phys. Rev. Lett. 110(3), 030502 (2013).
[Crossref]

G. Ferrini, J. P. Gazeau, T. Coudreau, C. Fabre, and N. Treps, “Compact gaussian quantum computation by multi-pixel homodyne detection,” New J. Phys. 15(9), 093015 (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(5), 378–381 (2013).
[Crossref]

2012 (3)

V. C. Usenko, B. Heim, C. Peuntinger, C. Wittmann, C. Marquardt, G. Leuchs, and R. Filip, “Entanglement of gaussian states and the applicability to quantum key distribution over fading channels,” New J. Phys. 14(9), 093048 (2012).
[Crossref]

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84(2), 621–669 (2012).
[Crossref]

L. S. Madsen, V. C. Usenko, M. Lassen, R. Filip, and U. L. Andersen, “Continuous variable quantum key distribution with modulated entangled states,” Nat. Commun. 3(1), 1083 (2012).
[Crossref]

2011 (2)

V. C. Usenko and R. Filip, “Squeezed-state quantum key distribution upon imperfect reconciliation,” New J. Phys. 13(11), 113007 (2011).
[Crossref]

P. Jouguet, S. Kunz-Jacques, and A. Leverrier, “Long-distance continuous-variable quantum key distribution with a gaussian modulation,” Phys. Rev. A 84(6), 062317 (2011).
[Crossref]

2010 (1)

A. Leverrier, F. Grosshans, and P. Grangier, “Finite-size analysis of a continuous-variable quantum key distribution,” Phys. Rev. A 81(6), 062343 (2010).
[Crossref]

2009 (3)

T. Iskhakov, M. V. Chekhova, and G. Leuchs, “Generation and direct detection of broadband mesoscopic polarization-squeezed vacuum,” Phys. Rev. Lett. 102(18), 183602 (2009).
[Crossref]

R. García-Patrón and N. J. Cerf, “Continuous-variable quantum key distribution protocols over noisy channels,” Phys. Rev. Lett. 102(13), 130501 (2009).
[Crossref]

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81(3), 1301–1350 (2009).
[Crossref]

2007 (1)

J. Lodewyck, M. Bloch, R. García-Patrón, 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(4), 042305 (2007).
[Crossref]

2005 (1)

H.-K. Lo, X. Ma, and K. Chen, “Decoy state quantum key distribution,” Phys. Rev. Lett. 94(23), 230504 (2005).
[Crossref]

2004 (1)

C. Weedbrook, A. M. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam, “Quantum cryptography without switching,” Phys. Rev. Lett. 93(17), 170504 (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(6920), 238–241 (2003).
[Crossref]

2002 (2)

F. Grosshans and P. Grangier, “Continuous variable quantum cryptography using coherent states,” Phys. Rev. Lett. 88(5), 057902 (2002).
[Crossref]

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002).
[Crossref]

1999 (1)

T. C. Ralph, “Continuous variable quantum cryptography,” Phys. Rev. A 61(1), 010303 (1999).
[Crossref]

Andersen, U. L.

L. S. Madsen, V. C. Usenko, M. Lassen, R. Filip, and U. L. Andersen, “Continuous variable quantum key distribution with modulated entangled states,” Nat. Commun. 3(1), 1083 (2012).
[Crossref]

S. Pirandola, U. L. Andersen, L. Banchi, M. Berta, D. Bunandar, R. Colbeck, D. Englund, T. Gehring, C. Lupo, C. Ottaviani, J. Pereira, M. Razavi, J. S. Shaari, M. Tomamichel, V. C. Usenko, G. Vallone, P. Villoresi, and P. Wallden, “Advances in quantum cryptography,” arXiv:1906.01645[quant-ph] (2019).

Awaji, Y.

T. A. Eriksson, T. Hirano, B. J. Puttnam, G. Rademacher, R. S. Luís, M. Fujiwara, R. Namiki, Y. Awaji, M. Takeoka, N. Wada, and M. Sasaki, “Wavelength division multiplexing of continuous variable quantum key distribution and 18.3 tbit/s data channels,” Commun. Phys. 2(1), 9 (2019).
[Crossref]

Banchi, L.

S. Pirandola, U. L. Andersen, L. Banchi, M. Berta, D. Bunandar, R. Colbeck, D. Englund, T. Gehring, C. Lupo, C. Ottaviani, J. Pereira, M. Razavi, J. S. Shaari, M. Tomamichel, V. C. Usenko, G. Vallone, P. Villoresi, and P. Wallden, “Advances in quantum cryptography,” arXiv:1906.01645[quant-ph] (2019).

Bayraktar, O.

D. Vasylyev, A. A. Semenov, W. Vogel, K. Günthner, A. Thurn, O. Bayraktar, and C. Marquardt, “Free-space quantum links under diverse weather conditions,” Phys. Rev. A 96(4), 043856 (2017).
[Crossref]

Bechmann-Pasquinucci, H.

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81(3), 1301–1350 (2009).
[Crossref]

Bello, L.

Y. Shaked, Y. Michael, R. Z. Vered, L. Bello, M. Rosenbluh, and A. Pe’er, “Lifting the bandwidth limit of optical homodyne measurement with broadband parametric amplification,” Nat. Commun. 9(1), 609 (2018).
[Crossref]

Bennett, C. H.

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

Berta, M.

S. Pirandola, U. L. Andersen, L. Banchi, M. Berta, D. Bunandar, R. Colbeck, D. Englund, T. Gehring, C. Lupo, C. Ottaviani, J. Pereira, M. Razavi, J. S. Shaari, M. Tomamichel, V. C. Usenko, G. Vallone, P. Villoresi, and P. Wallden, “Advances in quantum cryptography,” arXiv:1906.01645[quant-ph] (2019).

Bloch, M.

J. Lodewyck, M. Bloch, R. García-Patrón, 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(4), 042305 (2007).
[Crossref]

Bobrek, M.

B. Qi, P. Lougovski, R. Pooser, W. Grice, and M. Bobrek, “Generating the local oscillator “locally” in continuous-variable quantum key distribution based on coherent detection,” Phys. Rev. X 5(4), 041009 (2015).
[Crossref]

Bowen, W. P.

C. Weedbrook, A. M. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam, “Quantum cryptography without switching,” Phys. Rev. Lett. 93(17), 170504 (2004).
[Crossref]

Brassard, G.

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

Brif, C.

D. B. S. Soh, C. Brif, P. J. Coles, N. Lütkenhaus, R. M. Camacho, J. Urayama, and M. Sarovar, “Self-referenced continuous-variable quantum key distribution protocol,” Phys. Rev. X 5(4), 041010 (2015).
[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(6920), 238–241 (2003).
[Crossref]

Bunandar, D.

S. Pirandola, U. L. Andersen, L. Banchi, M. Berta, D. Bunandar, R. Colbeck, D. Englund, T. Gehring, C. Lupo, C. Ottaviani, J. Pereira, M. Razavi, J. S. Shaari, M. Tomamichel, V. C. Usenko, G. Vallone, P. Villoresi, and P. Wallden, “Advances in quantum cryptography,” arXiv:1906.01645[quant-ph] (2019).

Camacho, R. M.

D. B. S. Soh, C. Brif, P. J. Coles, N. Lütkenhaus, R. M. Camacho, J. Urayama, and M. Sarovar, “Self-referenced continuous-variable quantum key distribution protocol,” Phys. Rev. X 5(4), 041010 (2015).
[Crossref]

Cerf, N. J.

A. Leverrier, R. García-Patrón, R. Renner, and N. J. Cerf, “Security of continuous-variable quantum key distribution against general attacks,” Phys. Rev. Lett. 110(3), 030502 (2013).
[Crossref]

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84(2), 621–669 (2012).
[Crossref]

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81(3), 1301–1350 (2009).
[Crossref]

R. García-Patrón and N. J. Cerf, “Continuous-variable quantum key distribution protocols over noisy channels,” Phys. Rev. Lett. 102(13), 130501 (2009).
[Crossref]

J. Lodewyck, M. Bloch, R. García-Patrón, 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(4), 042305 (2007).
[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(6920), 238–241 (2003).
[Crossref]

Chekhova, M. V.

T. Iskhakov, M. V. Chekhova, and G. Leuchs, “Generation and direct detection of broadband mesoscopic polarization-squeezed vacuum,” Phys. Rev. Lett. 102(18), 183602 (2009).
[Crossref]

Chen, K.

H.-K. Lo, X. Ma, and K. Chen, “Decoy state quantum key distribution,” Phys. Rev. Lett. 94(23), 230504 (2005).
[Crossref]

Colbeck, R.

S. Pirandola, U. L. Andersen, L. Banchi, M. Berta, D. Bunandar, R. Colbeck, D. Englund, T. Gehring, C. Lupo, C. Ottaviani, J. Pereira, M. Razavi, J. S. Shaari, M. Tomamichel, V. C. Usenko, G. Vallone, P. Villoresi, and P. Wallden, “Advances in quantum cryptography,” arXiv:1906.01645[quant-ph] (2019).

Coles, P. J.

D. B. S. Soh, C. Brif, P. J. Coles, N. Lütkenhaus, R. M. Camacho, J. Urayama, and M. Sarovar, “Self-referenced continuous-variable quantum key distribution protocol,” Phys. Rev. X 5(4), 041010 (2015).
[Crossref]

Coudreau, T.

G. Ferrini, J. P. Gazeau, T. Coudreau, C. Fabre, and N. Treps, “Compact gaussian quantum computation by multi-pixel homodyne detection,” New J. Phys. 15(9), 093015 (2013).
[Crossref]

Debuisschert, T.

J. Lodewyck, M. Bloch, R. García-Patrón, 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(4), 042305 (2007).
[Crossref]

Derkach, I.

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V. C. Usenko, B. Heim, C. Peuntinger, C. Wittmann, C. Marquardt, G. Leuchs, and R. Filip, “Entanglement of gaussian states and the applicability to quantum key distribution over fading channels,” New J. Phys. 14(9), 093048 (2012).
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G. Ferrini, J. P. Gazeau, T. Coudreau, C. Fabre, and N. Treps, “Compact gaussian quantum computation by multi-pixel homodyne detection,” New J. Phys. 15(9), 093015 (2013).
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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(5), 378–381 (2013).
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B. Qi, P. Lougovski, R. Pooser, W. Grice, and M. Bobrek, “Generating the local oscillator “locally” in continuous-variable quantum key distribution based on coherent detection,” Phys. Rev. X 5(4), 041009 (2015).
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V. C. Usenko, B. Heim, C. Peuntinger, C. Wittmann, C. Marquardt, G. Leuchs, and R. Filip, “Entanglement of gaussian states and the applicability to quantum key distribution over fading channels,” New J. Phys. 14(9), 093048 (2012).
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P. Jouguet, S. Kunz-Jacques, and A. Leverrier, “Long-distance continuous-variable quantum key distribution with a gaussian modulation,” Phys. Rev. A 84(6), 062317 (2011).
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J. Lodewyck, M. Bloch, R. García-Patrón, 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(4), 042305 (2007).
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P. Jouguet, S. Kunz-Jacques, and A. Leverrier, “Long-distance continuous-variable quantum key distribution with a gaussian modulation,” Phys. Rev. A 84(6), 062317 (2011).
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C. Weedbrook, A. M. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam, “Quantum cryptography without switching,” Phys. Rev. Lett. 93(17), 170504 (2004).
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C. Weedbrook, A. M. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam, “Quantum cryptography without switching,” Phys. Rev. Lett. 93(17), 170504 (2004).
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M. Lasota, R. Filip, and V. C. Usenko, “Robustness of quantum key distribution with discrete and continuous variables to channel noise,” Phys. Rev. A 95(6), 062312 (2017).
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L. S. Madsen, V. C. Usenko, M. Lassen, R. Filip, and U. L. Andersen, “Continuous variable quantum key distribution with modulated entangled states,” Nat. Commun. 3(1), 1083 (2012).
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V. C. Usenko, B. Heim, C. Peuntinger, C. Wittmann, C. Marquardt, G. Leuchs, and R. Filip, “Entanglement of gaussian states and the applicability to quantum key distribution over fading channels,” New J. Phys. 14(9), 093048 (2012).
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T. Iskhakov, M. V. Chekhova, and G. Leuchs, “Generation and direct detection of broadband mesoscopic polarization-squeezed vacuum,” Phys. Rev. Lett. 102(18), 183602 (2009).
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A. Leverrier, R. García-Patrón, R. Renner, and N. J. Cerf, “Security of continuous-variable quantum key distribution against general attacks,” Phys. Rev. Lett. 110(3), 030502 (2013).
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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(5), 378–381 (2013).
[Crossref]

P. Jouguet, S. Kunz-Jacques, and A. Leverrier, “Long-distance continuous-variable quantum key distribution with a gaussian modulation,” Phys. Rev. A 84(6), 062317 (2011).
[Crossref]

A. Leverrier, F. Grosshans, and P. Grangier, “Finite-size analysis of a continuous-variable quantum key distribution,” Phys. Rev. A 81(6), 062343 (2010).
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Liu, W.

Lloyd, S.

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84(2), 621–669 (2012).
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E. Diamanti, H.-K. Lo, B. Qi, and Z. Yuan, “Practical challenges in quantum key distribution,” npj Quantum Inf. 2(1), 16025 (2016).
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H.-K. Lo, X. Ma, and K. Chen, “Decoy state quantum key distribution,” Phys. Rev. Lett. 94(23), 230504 (2005).
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J. Lodewyck, M. Bloch, R. García-Patrón, 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(4), 042305 (2007).
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Lougovski, P.

B. Qi, P. Lougovski, R. Pooser, W. Grice, and M. Bobrek, “Generating the local oscillator “locally” in continuous-variable quantum key distribution based on coherent detection,” Phys. Rev. X 5(4), 041009 (2015).
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T. A. Eriksson, T. Hirano, B. J. Puttnam, G. Rademacher, R. S. Luís, M. Fujiwara, R. Namiki, Y. Awaji, M. Takeoka, N. Wada, and M. Sasaki, “Wavelength division multiplexing of continuous variable quantum key distribution and 18.3 tbit/s data channels,” Commun. Phys. 2(1), 9 (2019).
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S. Pirandola, U. L. Andersen, L. Banchi, M. Berta, D. Bunandar, R. Colbeck, D. Englund, T. Gehring, C. Lupo, C. Ottaviani, J. Pereira, M. Razavi, J. S. Shaari, M. Tomamichel, V. C. Usenko, G. Vallone, P. Villoresi, and P. Wallden, “Advances in quantum cryptography,” arXiv:1906.01645[quant-ph] (2019).

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D. B. S. Soh, C. Brif, P. J. Coles, N. Lütkenhaus, R. M. Camacho, J. Urayama, and M. Sarovar, “Self-referenced continuous-variable quantum key distribution protocol,” Phys. Rev. X 5(4), 041010 (2015).
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V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81(3), 1301–1350 (2009).
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H.-K. Lo, X. Ma, and K. Chen, “Decoy state quantum key distribution,” Phys. Rev. Lett. 94(23), 230504 (2005).
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L. S. Madsen, V. C. Usenko, M. Lassen, R. Filip, and U. L. Andersen, “Continuous variable quantum key distribution with modulated entangled states,” Nat. Commun. 3(1), 1083 (2012).
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D. Vasylyev, A. A. Semenov, W. Vogel, K. Günthner, A. Thurn, O. Bayraktar, and C. Marquardt, “Free-space quantum links under diverse weather conditions,” Phys. Rev. A 96(4), 043856 (2017).
[Crossref]

V. C. Usenko, B. Heim, C. Peuntinger, C. Wittmann, C. Marquardt, G. Leuchs, and R. Filip, “Entanglement of gaussian states and the applicability to quantum key distribution over fading channels,” New J. Phys. 14(9), 093048 (2012).
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J. Lodewyck, M. Bloch, R. García-Patrón, 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(4), 042305 (2007).
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T. A. Eriksson, T. Hirano, B. J. Puttnam, G. Rademacher, R. S. Luís, M. Fujiwara, R. Namiki, Y. Awaji, M. Takeoka, N. Wada, and M. Sasaki, “Wavelength division multiplexing of continuous variable quantum key distribution and 18.3 tbit/s data channels,” Commun. Phys. 2(1), 9 (2019).
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S. Pirandola, U. L. Andersen, L. Banchi, M. Berta, D. Bunandar, R. Colbeck, D. Englund, T. Gehring, C. Lupo, C. Ottaviani, J. Pereira, M. Razavi, J. S. Shaari, M. Tomamichel, V. C. Usenko, G. Vallone, P. Villoresi, and P. Wallden, “Advances in quantum cryptography,” arXiv:1906.01645[quant-ph] (2019).

Pe’er, A.

Y. Shaked, Y. Michael, R. Z. Vered, L. Bello, M. Rosenbluh, and A. Pe’er, “Lifting the bandwidth limit of optical homodyne measurement with broadband parametric amplification,” Nat. Commun. 9(1), 609 (2018).
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Peev, M.

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81(3), 1301–1350 (2009).
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Pereira, J.

S. Pirandola, U. L. Andersen, L. Banchi, M. Berta, D. Bunandar, R. Colbeck, D. Englund, T. Gehring, C. Lupo, C. Ottaviani, J. Pereira, M. Razavi, J. S. Shaari, M. Tomamichel, V. C. Usenko, G. Vallone, P. Villoresi, and P. Wallden, “Advances in quantum cryptography,” arXiv:1906.01645[quant-ph] (2019).

Peuntinger, C.

V. C. Usenko, B. Heim, C. Peuntinger, C. Wittmann, C. Marquardt, G. Leuchs, and R. Filip, “Entanglement of gaussian states and the applicability to quantum key distribution over fading channels,” New J. Phys. 14(9), 093048 (2012).
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Pirandola, S.

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84(2), 621–669 (2012).
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S. Pirandola, U. L. Andersen, L. Banchi, M. Berta, D. Bunandar, R. Colbeck, D. Englund, T. Gehring, C. Lupo, C. Ottaviani, J. Pereira, M. Razavi, J. S. Shaari, M. Tomamichel, V. C. Usenko, G. Vallone, P. Villoresi, and P. Wallden, “Advances in quantum cryptography,” arXiv:1906.01645[quant-ph] (2019).

Pooser, R.

B. Qi, P. Lougovski, R. Pooser, W. Grice, and M. Bobrek, “Generating the local oscillator “locally” in continuous-variable quantum key distribution based on coherent detection,” Phys. Rev. X 5(4), 041009 (2015).
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T. A. Eriksson, T. Hirano, B. J. Puttnam, G. Rademacher, R. S. Luís, M. Fujiwara, R. Namiki, Y. Awaji, M. Takeoka, N. Wada, and M. Sasaki, “Wavelength division multiplexing of continuous variable quantum key distribution and 18.3 tbit/s data channels,” Commun. Phys. 2(1), 9 (2019).
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Qi, B.

E. Diamanti, H.-K. Lo, B. Qi, and Z. Yuan, “Practical challenges in quantum key distribution,” npj Quantum Inf. 2(1), 16025 (2016).
[Crossref]

B. Qi, P. Lougovski, R. Pooser, W. Grice, and M. Bobrek, “Generating the local oscillator “locally” in continuous-variable quantum key distribution based on coherent detection,” Phys. Rev. X 5(4), 041009 (2015).
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T. A. Eriksson, T. Hirano, B. J. Puttnam, G. Rademacher, R. S. Luís, M. Fujiwara, R. Namiki, Y. Awaji, M. Takeoka, N. Wada, and M. Sasaki, “Wavelength division multiplexing of continuous variable quantum key distribution and 18.3 tbit/s data channels,” Commun. Phys. 2(1), 9 (2019).
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C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84(2), 621–669 (2012).
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T. C. Ralph, “Continuous variable quantum cryptography,” Phys. Rev. A 61(1), 010303 (1999).
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Razavi, M.

S. Pirandola, U. L. Andersen, L. Banchi, M. Berta, D. Bunandar, R. Colbeck, D. Englund, T. Gehring, C. Lupo, C. Ottaviani, J. Pereira, M. Razavi, J. S. Shaari, M. Tomamichel, V. C. Usenko, G. Vallone, P. Villoresi, and P. Wallden, “Advances in quantum cryptography,” arXiv:1906.01645[quant-ph] (2019).

Renner, R.

A. Leverrier, R. García-Patrón, R. Renner, and N. J. Cerf, “Security of continuous-variable quantum key distribution against general attacks,” Phys. Rev. Lett. 110(3), 030502 (2013).
[Crossref]

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N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002).
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Rosenbluh, M.

Y. Shaked, Y. Michael, R. Z. Vered, L. Bello, M. Rosenbluh, and A. Pe’er, “Lifting the bandwidth limit of optical homodyne measurement with broadband parametric amplification,” Nat. Commun. 9(1), 609 (2018).
[Crossref]

Ruppert, L.

V. C. Usenko, L. Ruppert, and R. Filip, “Quantum communication with macroscopically bright nonclassical states,” Opt. Express 23(24), 31534–31543 (2015).
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V. C. Usenko, L. Ruppert, and R. Filip, “Entanglement-based continuous-variable quantum key distribution with multimode states and detectors,” Phys. Rev. A 90(6), 062326 (2014).
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Sarovar, M.

D. B. S. Soh, C. Brif, P. J. Coles, N. Lütkenhaus, R. M. Camacho, J. Urayama, and M. Sarovar, “Self-referenced continuous-variable quantum key distribution protocol,” Phys. Rev. X 5(4), 041010 (2015).
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Sasaki, M.

T. A. Eriksson, T. Hirano, B. J. Puttnam, G. Rademacher, R. S. Luís, M. Fujiwara, R. Namiki, Y. Awaji, M. Takeoka, N. Wada, and M. Sasaki, “Wavelength division multiplexing of continuous variable quantum key distribution and 18.3 tbit/s data channels,” Commun. Phys. 2(1), 9 (2019).
[Crossref]

Scarani, V.

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81(3), 1301–1350 (2009).
[Crossref]

Semenov, A. A.

D. Vasylyev, A. A. Semenov, W. Vogel, K. Günthner, A. Thurn, O. Bayraktar, and C. Marquardt, “Free-space quantum links under diverse weather conditions,” Phys. Rev. A 96(4), 043856 (2017).
[Crossref]

Shaari, J. S.

S. Pirandola, U. L. Andersen, L. Banchi, M. Berta, D. Bunandar, R. Colbeck, D. Englund, T. Gehring, C. Lupo, C. Ottaviani, J. Pereira, M. Razavi, J. S. Shaari, M. Tomamichel, V. C. Usenko, G. Vallone, P. Villoresi, and P. Wallden, “Advances in quantum cryptography,” arXiv:1906.01645[quant-ph] (2019).

Shaked, Y.

Y. Shaked, Y. Michael, R. Z. Vered, L. Bello, M. Rosenbluh, and A. Pe’er, “Lifting the bandwidth limit of optical homodyne measurement with broadband parametric amplification,” Nat. Commun. 9(1), 609 (2018).
[Crossref]

Shapiro, J. H.

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84(2), 621–669 (2012).
[Crossref]

Soh, D. B. S.

D. B. S. Soh, C. Brif, P. J. Coles, N. Lütkenhaus, R. M. Camacho, J. Urayama, and M. Sarovar, “Self-referenced continuous-variable quantum key distribution protocol,” Phys. Rev. X 5(4), 041010 (2015).
[Crossref]

Symul, T.

C. Weedbrook, A. M. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam, “Quantum cryptography without switching,” Phys. Rev. Lett. 93(17), 170504 (2004).
[Crossref]

Takeoka, M.

T. A. Eriksson, T. Hirano, B. J. Puttnam, G. Rademacher, R. S. Luís, M. Fujiwara, R. Namiki, Y. Awaji, M. Takeoka, N. Wada, and M. Sasaki, “Wavelength division multiplexing of continuous variable quantum key distribution and 18.3 tbit/s data channels,” Commun. Phys. 2(1), 9 (2019).
[Crossref]

Thurn, A.

D. Vasylyev, A. A. Semenov, W. Vogel, K. Günthner, A. Thurn, O. Bayraktar, and C. Marquardt, “Free-space quantum links under diverse weather conditions,” Phys. Rev. A 96(4), 043856 (2017).
[Crossref]

Tittel, W.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002).
[Crossref]

Tomamichel, M.

S. Pirandola, U. L. Andersen, L. Banchi, M. Berta, D. Bunandar, R. Colbeck, D. Englund, T. Gehring, C. Lupo, C. Ottaviani, J. Pereira, M. Razavi, J. S. Shaari, M. Tomamichel, V. C. Usenko, G. Vallone, P. Villoresi, and P. Wallden, “Advances in quantum cryptography,” arXiv:1906.01645[quant-ph] (2019).

Treps, N.

G. Ferrini, J. P. Gazeau, T. Coudreau, C. Fabre, and N. Treps, “Compact gaussian quantum computation by multi-pixel homodyne detection,” New J. Phys. 15(9), 093015 (2013).
[Crossref]

Tualle-Brouri, R.

J. Lodewyck, M. Bloch, R. García-Patrón, 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(4), 042305 (2007).
[Crossref]

Urayama, J.

D. B. S. Soh, C. Brif, P. J. Coles, N. Lütkenhaus, R. M. Camacho, J. Urayama, and M. Sarovar, “Self-referenced continuous-variable quantum key distribution protocol,” Phys. Rev. X 5(4), 041010 (2015).
[Crossref]

Usenko, V. C.

M. Lasota, R. Filip, and V. C. Usenko, “Robustness of quantum key distribution with discrete and continuous variables to channel noise,” Phys. Rev. A 95(6), 062312 (2017).
[Crossref]

I. Derkach, V. C. Usenko, and R. Filip, “Continuous-variable quantum key distribution with a leakage from state preparation,” Phys. Rev. A 96(6), 062309 (2017).
[Crossref]

V. C. Usenko and R. Filip, “Trusted noise in continuous-variable quantum key distribution: A threat and a defense,” Entropy 18(1), 20 (2016).
[Crossref]

I. Derkach, V. C. Usenko, and R. Filip, “Preventing side-channel effects in continuous-variable quantum key distribution,” Phys. Rev. A 93(3), 032309 (2016).
[Crossref]

V. C. Usenko, L. Ruppert, and R. Filip, “Quantum communication with macroscopically bright nonclassical states,” Opt. Express 23(24), 31534–31543 (2015).
[Crossref]

V. C. Usenko and F. Grosshans, “Unidimensional continuous-variable quantum key distribution,” Phys. Rev. A 92(6), 062337 (2015).
[Crossref]

V. C. Usenko, L. Ruppert, and R. Filip, “Entanglement-based continuous-variable quantum key distribution with multimode states and detectors,” Phys. Rev. A 90(6), 062326 (2014).
[Crossref]

L. S. Madsen, V. C. Usenko, M. Lassen, R. Filip, and U. L. Andersen, “Continuous variable quantum key distribution with modulated entangled states,” Nat. Commun. 3(1), 1083 (2012).
[Crossref]

V. C. Usenko, B. Heim, C. Peuntinger, C. Wittmann, C. Marquardt, G. Leuchs, and R. Filip, “Entanglement of gaussian states and the applicability to quantum key distribution over fading channels,” New J. Phys. 14(9), 093048 (2012).
[Crossref]

V. C. Usenko and R. Filip, “Squeezed-state quantum key distribution upon imperfect reconciliation,” New J. Phys. 13(11), 113007 (2011).
[Crossref]

S. Pirandola, U. L. Andersen, L. Banchi, M. Berta, D. Bunandar, R. Colbeck, D. Englund, T. Gehring, C. Lupo, C. Ottaviani, J. Pereira, M. Razavi, J. S. Shaari, M. Tomamichel, V. C. Usenko, G. Vallone, P. Villoresi, and P. Wallden, “Advances in quantum cryptography,” arXiv:1906.01645[quant-ph] (2019).

I. Derkach, V. C. Usenko, and R. Filip, “Squeezing-enhanced quantum key distribution over atmospheric channels,” arXiv:1809.10167 [quant-ph] (2018).

Vallone, G.

S. Pirandola, U. L. Andersen, L. Banchi, M. Berta, D. Bunandar, R. Colbeck, D. Englund, T. Gehring, C. Lupo, C. Ottaviani, J. Pereira, M. Razavi, J. S. Shaari, M. Tomamichel, V. C. Usenko, G. Vallone, P. Villoresi, and P. Wallden, “Advances in quantum cryptography,” arXiv:1906.01645[quant-ph] (2019).

Van Assche, G.

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(6920), 238–241 (2003).
[Crossref]

Vasylyev, D.

D. Vasylyev, A. A. Semenov, W. Vogel, K. Günthner, A. Thurn, O. Bayraktar, and C. Marquardt, “Free-space quantum links under diverse weather conditions,” Phys. Rev. A 96(4), 043856 (2017).
[Crossref]

Vered, R. Z.

Y. Shaked, Y. Michael, R. Z. Vered, L. Bello, M. Rosenbluh, and A. Pe’er, “Lifting the bandwidth limit of optical homodyne measurement with broadband parametric amplification,” Nat. Commun. 9(1), 609 (2018).
[Crossref]

Villoresi, P.

S. Pirandola, U. L. Andersen, L. Banchi, M. Berta, D. Bunandar, R. Colbeck, D. Englund, T. Gehring, C. Lupo, C. Ottaviani, J. Pereira, M. Razavi, J. S. Shaari, M. Tomamichel, V. C. Usenko, G. Vallone, P. Villoresi, and P. Wallden, “Advances in quantum cryptography,” arXiv:1906.01645[quant-ph] (2019).

Vogel, W.

D. Vasylyev, A. A. Semenov, W. Vogel, K. Günthner, A. Thurn, O. Bayraktar, and C. Marquardt, “Free-space quantum links under diverse weather conditions,” Phys. Rev. A 96(4), 043856 (2017).
[Crossref]

Wada, N.

T. A. Eriksson, T. Hirano, B. J. Puttnam, G. Rademacher, R. S. Luís, M. Fujiwara, R. Namiki, Y. Awaji, M. Takeoka, N. Wada, and M. Sasaki, “Wavelength division multiplexing of continuous variable quantum key distribution and 18.3 tbit/s data channels,” Commun. Phys. 2(1), 9 (2019).
[Crossref]

Wallden, P.

S. Pirandola, U. L. Andersen, L. Banchi, M. Berta, D. Bunandar, R. Colbeck, D. Englund, T. Gehring, C. Lupo, C. Ottaviani, J. Pereira, M. Razavi, J. S. Shaari, M. Tomamichel, V. C. Usenko, G. Vallone, P. Villoresi, and P. Wallden, “Advances in quantum cryptography,” arXiv:1906.01645[quant-ph] (2019).

Wang, C.

Weedbrook, C.

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84(2), 621–669 (2012).
[Crossref]

C. Weedbrook, A. M. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam, “Quantum cryptography without switching,” Phys. Rev. Lett. 93(17), 170504 (2004).
[Crossref]

Wenger, J.

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(6920), 238–241 (2003).
[Crossref]

Wittmann, C.

V. C. Usenko, B. Heim, C. Peuntinger, C. Wittmann, C. Marquardt, G. Leuchs, and R. Filip, “Entanglement of gaussian states and the applicability to quantum key distribution over fading channels,” New J. Phys. 14(9), 093048 (2012).
[Crossref]

Yuan, Z.

E. Diamanti, H.-K. Lo, B. Qi, and Z. Yuan, “Practical challenges in quantum key distribution,” npj Quantum Inf. 2(1), 16025 (2016).
[Crossref]

Zbinden, H.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002).
[Crossref]

Zeng, G.

Commun. Phys. (1)

T. A. Eriksson, T. Hirano, B. J. Puttnam, G. Rademacher, R. S. Luís, M. Fujiwara, R. Namiki, Y. Awaji, M. Takeoka, N. Wada, and M. Sasaki, “Wavelength division multiplexing of continuous variable quantum key distribution and 18.3 tbit/s data channels,” Commun. Phys. 2(1), 9 (2019).
[Crossref]

Entropy (1)

V. C. Usenko and R. Filip, “Trusted noise in continuous-variable quantum key distribution: A threat and a defense,” Entropy 18(1), 20 (2016).
[Crossref]

Nat. Commun. (2)

Y. Shaked, Y. Michael, R. Z. Vered, L. Bello, M. Rosenbluh, and A. Pe’er, “Lifting the bandwidth limit of optical homodyne measurement with broadband parametric amplification,” Nat. Commun. 9(1), 609 (2018).
[Crossref]

L. S. Madsen, V. C. Usenko, M. Lassen, R. Filip, and U. L. Andersen, “Continuous variable quantum key distribution with modulated entangled states,” Nat. Commun. 3(1), 1083 (2012).
[Crossref]

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(5), 378–381 (2013).
[Crossref]

Nature (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(6920), 238–241 (2003).
[Crossref]

New J. Phys. (3)

V. C. Usenko, B. Heim, C. Peuntinger, C. Wittmann, C. Marquardt, G. Leuchs, and R. Filip, “Entanglement of gaussian states and the applicability to quantum key distribution over fading channels,” New J. Phys. 14(9), 093048 (2012).
[Crossref]

G. Ferrini, J. P. Gazeau, T. Coudreau, C. Fabre, and N. Treps, “Compact gaussian quantum computation by multi-pixel homodyne detection,” New J. Phys. 15(9), 093015 (2013).
[Crossref]

V. C. Usenko and R. Filip, “Squeezed-state quantum key distribution upon imperfect reconciliation,” New J. Phys. 13(11), 113007 (2011).
[Crossref]

npj Quantum Inf. (1)

E. Diamanti, H.-K. Lo, B. Qi, and Z. Yuan, “Practical challenges in quantum key distribution,” npj Quantum Inf. 2(1), 16025 (2016).
[Crossref]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. A (10)

J. Lodewyck, M. Bloch, R. García-Patrón, 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(4), 042305 (2007).
[Crossref]

M. Lasota, R. Filip, and V. C. Usenko, “Robustness of quantum key distribution with discrete and continuous variables to channel noise,” Phys. Rev. A 95(6), 062312 (2017).
[Crossref]

V. C. Usenko, L. Ruppert, and R. Filip, “Entanglement-based continuous-variable quantum key distribution with multimode states and detectors,” Phys. Rev. A 90(6), 062326 (2014).
[Crossref]

T. C. Ralph, “Continuous variable quantum cryptography,” Phys. Rev. A 61(1), 010303 (1999).
[Crossref]

V. C. Usenko and F. Grosshans, “Unidimensional continuous-variable quantum key distribution,” Phys. Rev. A 92(6), 062337 (2015).
[Crossref]

I. Derkach, V. C. Usenko, and R. Filip, “Preventing side-channel effects in continuous-variable quantum key distribution,” Phys. Rev. A 93(3), 032309 (2016).
[Crossref]

I. Derkach, V. C. Usenko, and R. Filip, “Continuous-variable quantum key distribution with a leakage from state preparation,” Phys. Rev. A 96(6), 062309 (2017).
[Crossref]

A. Leverrier, F. Grosshans, and P. Grangier, “Finite-size analysis of a continuous-variable quantum key distribution,” Phys. Rev. A 81(6), 062343 (2010).
[Crossref]

D. Vasylyev, A. A. Semenov, W. Vogel, K. Günthner, A. Thurn, O. Bayraktar, and C. Marquardt, “Free-space quantum links under diverse weather conditions,” Phys. Rev. A 96(4), 043856 (2017).
[Crossref]

P. Jouguet, S. Kunz-Jacques, and A. Leverrier, “Long-distance continuous-variable quantum key distribution with a gaussian modulation,” Phys. Rev. A 84(6), 062317 (2011).
[Crossref]

Phys. Rev. Lett. (7)

A. Leverrier, “Security of continuous-variable quantum key distribution via a gaussian de finetti reduction,” Phys. Rev. Lett. 118(20), 200501 (2017).
[Crossref]

T. Iskhakov, M. V. Chekhova, and G. Leuchs, “Generation and direct detection of broadband mesoscopic polarization-squeezed vacuum,” Phys. Rev. Lett. 102(18), 183602 (2009).
[Crossref]

A. Leverrier, R. García-Patrón, R. Renner, and N. J. Cerf, “Security of continuous-variable quantum key distribution against general attacks,” Phys. Rev. Lett. 110(3), 030502 (2013).
[Crossref]

R. García-Patrón and N. J. Cerf, “Continuous-variable quantum key distribution protocols over noisy channels,” Phys. Rev. Lett. 102(13), 130501 (2009).
[Crossref]

F. Grosshans and P. Grangier, “Continuous variable quantum cryptography using coherent states,” Phys. Rev. Lett. 88(5), 057902 (2002).
[Crossref]

C. Weedbrook, A. M. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam, “Quantum cryptography without switching,” Phys. Rev. Lett. 93(17), 170504 (2004).
[Crossref]

H.-K. Lo, X. Ma, and K. Chen, “Decoy state quantum key distribution,” Phys. Rev. Lett. 94(23), 230504 (2005).
[Crossref]

Phys. Rev. X (2)

D. B. S. Soh, C. Brif, P. J. Coles, N. Lütkenhaus, R. M. Camacho, J. Urayama, and M. Sarovar, “Self-referenced continuous-variable quantum key distribution protocol,” Phys. Rev. X 5(4), 041010 (2015).
[Crossref]

B. Qi, P. Lougovski, R. Pooser, W. Grice, and M. Bobrek, “Generating the local oscillator “locally” in continuous-variable quantum key distribution based on coherent detection,” Phys. Rev. X 5(4), 041009 (2015).
[Crossref]

Rev. Mod. Phys. (3)

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002).
[Crossref]

V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Rev. Mod. Phys. 81(3), 1301–1350 (2009).
[Crossref]

C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, “Gaussian quantum information,” Rev. Mod. Phys. 84(2), 621–669 (2012).
[Crossref]

Sci. Rep. (1)

D. Huang, P. Huang, D. Lin, and G. Zeng, “Long-distance continuous-variable quantum key distribution by controlling excess noise,” Sci. Rep. 6(1), 19201 (2016).
[Crossref]

Other (3)

I. Derkach, V. C. Usenko, and R. Filip, “Squeezing-enhanced quantum key distribution over atmospheric channels,” arXiv:1809.10167 [quant-ph] (2018).

S. Pirandola, U. L. Andersen, L. Banchi, M. Berta, D. Bunandar, R. Colbeck, D. Englund, T. Gehring, C. Lupo, C. Ottaviani, J. Pereira, M. Razavi, J. S. Shaari, M. Tomamichel, V. C. Usenko, G. Vallone, P. Villoresi, and P. Wallden, “Advances in quantum cryptography,” arXiv:1906.01645[quant-ph] (2019).

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

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Figures (5)

Fig. 1.
Fig. 1. The standard scheme for homodyne detection (left) and the scheme with uncompensated modes in the multimode signal beam (right).
Fig. 2.
Fig. 2. The experimental setup used for the test of homodyne measurement of bright multimode coherent light.
Fig. 3.
Fig. 3. Dependence of the normalized variance in SNU, experimentally measured (points) and theoretically predicted, according to Eq. (3) (lines), on unmatched mode power (left panel) and on LO power (right panel).
Fig. 4.
Fig. 4. Normalized variance of the quadrature measurements in SNU in the absence and presence of matched $|\alpha \rangle$ and unmatched $|\beta \rangle$ modes, $|\beta |^2=0.16|\alpha _{LO}|^{2}$. Theoretical prediction according to Eq. (3) is given in blue dashed lines.
Fig. 5.
Fig. 5. Left: the key rate for multimode coherent-state CV QKD in the presence of mode mismatch versus the LO brightness at different values of the channel transmittance T, obtained from the experimentally measured noise (points with error bars) and from the calculated quadrature variance Eq. (1), $N/M=1$ (lines). The straight horizontal lines represent the ideal case where all the modes match perfectly. Right: the key rate for multimode coherent-state CV QKD in the presence of mode mismatch (theoretically evaluated using Eq. (1) for the given parameters) versus the unmatched mode brightness, $|\beta |^2$, when only the matched mode is modulated, or, equivalently, versus the number of unmatched modes, $N$, when all the modes are modulated, and the LO brigthness is varied, $T=0.5$. In both plots, the modulation variance is optimized, $\zeta =0.96$ and $\epsilon ^2=1$ as confirmed in the experiment.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

V a r ( x ) m e a s = V a r ( x ) + ε t o t 2 n ¯ ,
ε t o t 2 N ε 2 M | α L O | 2 ,
  V a r ( x ) m e a s = 1 + | β | 2 | α L O | 2 ,
K = m a x { 0 , ζ I A B χ B E } ,
γ A B = ( V I T ( V 2 1 ) σ z T ( V 2 1 ) σ z [ T ( V + V N ) + 1 T + ε t o t 2 n ¯ ] I ) ,