Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Continuous-variable quantum key distribution with a single quadrature measurement at an arbitrary reference frame

Vinod N. Rao1,2,*, Emma Tien Hwai Medlock1, Timothy Spiller1,2, and Rupesh Kumar1,2,†

  • 1School of Physics, Engineering & Technology and York Centre for Quantum Technologies, University of York, YO10 5FT York, United Kingdom
  • 2Quantum Communications Hub, University of York, United Kingdom

  • *Contact author: vinod.rao@york.ac.uk
  • †Contact author: rupesh.kumar@york.ac.uk

Phys. Rev. A 112, 042406 – Published 3 October, 2025

DOI: https://doi.org/10.1103/g465-pm47

Abstract

We propose a simplified measurement scheme for a Gaussian modulated coherent state (GMCS) protocol for continuous variable quantum key distribution (CV-QKD), utilizing homodyne detection without quadrature switching. The reference frame of measurement is taken to be at an arbitrary angle, however, reconciliation converges the proposed scheme to GMCS with switching quadrature protocol. The arbitrary frame of measurement could also include the unknown random thermal drift within Bob's optical measurement setup. We found this scheme is advantageous for practical free-space and fiber-based GMCS protocol-based CV-QKD systems as it does not require a phase modulator for random measurement selection quadrature at Bob.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (50)

  1. C. H. Bennett and G. Brassard, Quantum cryptography: Public key distribution and coin tossing, in Proceedings of the International Conference on Computers, Systems and Signal Processing (1984).
  2. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, Quantum cryptography, Rev. Mod. Phys. 74, 145 (2002).
  3. S. Pirandola, U. L. Andersen, L. Banchi, M. Berta, D. Bunandar, R. Colbeck, D. Englund, T. Gehring, C. Lupo, C. Ottaviani et al., Advances in quantum cryptography, Adv. Optics Photon. 12, 1012 (2020).
  4. W. K. Wootters and W. H. Zurek, A single quantum cannot be cloned, Nature (London) 299, 802 (1982).
  5. I. D. Ivanovic, How to differentiate between non-orthogonal states, Phys. Lett. A 123, 257 (1987).
  6. R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Quantum entanglement, Rev. Mod. Phys. 81, 865 (2009).
  7. M. Koashi, Unconditional security of quantum key distribution and the uncertainty principle, J. Phys. Conf. Ser. 36, 98 (2006).
  8. A. K. Ekert, Quantum cryptography based on Bell's theorem, Phys. Rev. Lett. 67, 661 (1991).
  9. C. H. Bennett, Quantum cryptography using any two nonorthogonal states, Phys. Rev. Lett. 68, 3121 (1992).
  10. C. Marand and P. D. Townsend, Quantum key distribution over distances as long as 30 km, Opt. Lett. 20, 1695 (1995).
  11. R. J. Hughes, G. L. Morgan, and C Glen Peterson, Quantum key distribution over a 48 km optical fibre network, J. Mod. Opt. 47, 533–547 (2000).
  12. D. Stucki, N. Gisin, O. Guinnard, G. Ribordy, and H. Zbinden, Quantum key distribution over 67 km with a plug&play system, New J. Phys. 4, 41 (2002).
  13. C. Wang, J. Zhang, P. Wang, F. Deng, Q. Al, and G. Long, Experimental realization of quantum cryptography communication in free space, Sci. China. Ser. G 48, 237 (2005).
  14. H.-K. Lo, M. Curty, and B. Qi, Measurement-device-independent quantum key distribution, Phys. Rev. Lett. 108, 130503 (2012).
  15. M. Lucamarini, Z. L. Yuan, J. F. Dynes, and A. J. Shields, Overcoming the rate–distance limit of quantum key distribution without quantum repeaters, Nature (London) 557, 400 (2018).
  16. S. Wang, Z.-Q. Yin, D.-Y. He, W. Chen, R.-Q. Wang, P. Ye, Y. Zhou, G.-J. Fan-Yuan, F.-X. Wang, W. Chen et al., Twin-field quantum key distribution over 830-km fibre, Nature Photon. 16, 154 (2022).
  17. T. C. Ralph, Continuous variable quantum cryptography, Phys. Rev. A 61, 010303(R) (1999).
  18. M. Hillery, Quantum cryptography with squeezed states, Phys. Rev. A 61, 022309 (2000).
  19. M. D. Reid, Quantum cryptography with a predetermined key, using continuous-variable einstein-podolsky-rosen correlations, Phys. Rev. A 62, 062308 (2000).
  20. Frédéric Grosshans and P. Grangier, Continuous variable quantum cryptography using coherent states, Phys. Rev. Lett. 88, 057902 (2002).
  21. S. L. Braunstein and P. Van Loock, Quantum information with continuous variables, Rev. Mod. Phys. 77, 513 (2005).
  22. 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, 170504 (2004).
  23. U. L. Andersen, G. Leuchs, and C. Silberhorn, Continuous-variable quantum information processing, Laser Photon. Rev. 4, 337 (2010).
  24. 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, 041010 (2015).
  25. Y. Zhang, Z. Li, Z. Chen, C. Weedbrook, Y. Zhao, X. Wang, Y. Huang, C. Xu, X. Zhang, Z. Wang et al., Continuous-variable qkd over 50 km commercial fiber, Quantum Sci. Technol. 4, 035006 (2019).
  26. P. Jouguet, Sébastien Kunz-Jacques, A. Leverrier, P. Grangier, and E. Diamanti, Experimental demonstration of long-distance continuous-variable quantum key distribution, Nat. Photon. 7, 378 (2013).
  27. D. Huang, P. Huang, D. Lin, and G. Zeng, Long-distance continuous-variable quantum key distribution by controlling excess noise, Sci. Rep. 6, 19201 (2016).
  28. Y. Zhang, Z. Chen, S. Pirandola, X. Wang, C. Zhou, B. Chu, Y. Zhao, B. Xu, S. Yu, and H. Guo, Long-distance continuous-variable quantum key distribution over 202.81 km of fiber, Phys. Rev. Lett. 125, 010502 (2020).
  29. C. Lupo, Towards practical security of continuous-variable quantum key distribution, Phys. Rev. A 102, 022623 (2020).
  30. N. Gisin, S. Fasel, B. Kraus, H. Zbinden, and Grégoire Ribordy, Trojan-horse attacks on quantum-key-distribution systems, Phys. Rev. A 73, 022320 (2006).
  31. H. Qin, R. Kumar, and R. Alléaume, Quantum hacking: Saturation attack on practical continuous-variable quantum key distribution, Phys. Rev. A 94, 012325 (2016).
  32. Z. Xing, X. Li, X. Ruan, Y. Luo, and H. Zhang, Phase compensation for continuous variable quantum key distribution based on convolutional neural network, in Photonics (MDPI, 2022), Vol. 9, p. 463.
  33. Y. Pan, L. Zhang, and D. Huang, Practical security bounds against trojan horse attacks in continuous-variable quantum key distribution, Appl. Sci. 10, 7788 (2020).
  34. F. Laudenbach, C. Pacher, Chi-Hang Fred Fung, A. Poppe, M. Peev, B. Schrenk, M. Hentschel, P. Walther, and H. Hübel, Continuous-variable quantum key distribution with gaussian modulation'the theory of practical implementations, Adv. Quantum Technol. 1, 1800011 (2018).
  35. C. Weedbrook, S. Pirandola, Raúl García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, Gaussian quantum information, Rev. Mod. Phys. 84, 621 (2012).
  36. X. Tang, R. Kumar, S. Ren, A. Wonfor, R. V. Penty, and I. H. White, Performance of continuous variable quantum key distribution system at different detector bandwidth, Opt. Commun. 471, 126034 (2020).
  37. S. J. A. G. Cosijns, M. J. Jansen, and H. Haitjema, Advanced optical incremental sensors: encoders and interferometers, in Smart sensors and MEMS (Elsevier, Amsterdam, 2018), pp. 245–290.
  38. X. Tang, R. Kumar, C. Sun, L. Zhang, Z. Chen, R. Jiang, H. Wang, and A. Zhang, Towards underwater coherent optical wireless communications using a simplified detection scheme, Opt. Express 29, 19340 (2021).
  39. X. Tang, Z. Chen, Z. Zhao, R. Kumar, and Y. Dong, Experimental study on underwater continuous-variable quantum key distribution with discrete modulation, Opt. Express 30, 32428 (2022).
  40. W.-B. Liu, C.-L. Li, Y.-M. Xie, C.-X. Weng, J. Gu, X.-Y. Cao, Y.-S. Lu, B.-H. Li, H.-L. Yin, and Z.-B. Chen, Homodyne detection quadrature phase shift keying continuous-variable quantum key distribution with high excess noise tolerance, PRX Quantum 2, 040334 (2021).
  41. N. Jain, H.-M. Chin, H. Mani, C. Lupo, D. S. Nikolic, A. Kordts, S. Pirandola, T. B. Pedersen, M. Kolb, B. Ömer et al., Practical continuous-variable quantum key distribution with composable security, Nat. Commun. 13, 4740 (2022).
  42. B. Qi, Simultaneous classical communication and quantum key distribution using continuous variables, Phys. Rev. A 94, 042340 (2016).
  43. A. Marie and R. Alléaume, Self-coherent phase reference sharing for continuous-variable quantum key distribution, Phys. Rev. A 95, 012316 (2017).
  44. C. H. Bennett, F. Bessette, G. Brassard, L. Salvail, and J. Smolin, Experimental quantum cryptography, J. Cryptol. 5, 3 (1992).
  45. Y. Zhang, Y. Bian, Z. Li, S. Yu, and H. Guo, Continuous-variable quantum key distribution system: Past, present, and future, Appl. Phys. Rev. 11 (2024).
  46. V. C. Usenko and Frédéric Grosshans, Unidimensional continuous-variable quantum key distribution, Phys. Rev. A 92, 062337 (2015).
  47. V. C. Usenko, Unidimensional continuous-variable quantum key distribution using squeezed states, Phys. Rev. A 98, 032321 (2018).
  48. P. Wang, X. Wang, and Y. Li, Security analysis of unidimensional continuous-variable quantum key distribution using uncertainty relations, Entropy 20, 157 (2018).
  49. D. Bai, P. Huang, Y. Zhu, H. Ma, T. Xiao, T. Wang, and G. Zeng, Unidimensional continuous-variable measurement-device-independent quantum key distribution, Quantum Info. Proc. 19, 1 (2020).
  50. W. Liu, J. Peng, P. Huang, S. Wang, T. Wang, and G. Zeng, Continuous-variable quantum key distribution based on continuous random basis choice, Chin. Phys. B 27, 070305 (2018).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation