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  • Open Access

High-Rate Discrete-Modulated Continuous-Variable Quantum Key Distribution with Composable Security

Mingze Wu1,*, Yan Pan2,*, Junhui Li1, Heng Wang2, Lu Fan1, Yun Shao2, Yang Li2, Wei Huang2, Song Yu1 et al.

Bingjie Xu2,† and Yichen Zhang1,‡

  • 1State Key Laboratory of Information Photonics and Optical Communications, School of Electronic Engineering, Beijing University of Posts and Telecommunications, Beijing 100876, China
  • 2National Key Laboratory of Security Communication, Institute of Southwestern Communication, Chengdu 610041, China

  • *These authors contributed equally to this work.
  • †Contact author: xbjpku@163.com
  • ‡Contact author: zhangyc@bupt.edu.cn
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Phys. Rev. X 16, 021039 – Published 20 May, 2026

DOI: https://doi.org/10.1103/882y-w4zy

Abstract

Continuous-variable quantum key distribution holds the potential to generate high secret key rates, making it a prime candidate for high-rate metropolitan quantum network applications. However, despite these promising opportunities, the realization of high-rate continuous-variable quantum key distribution systems with composable security remains an elusive goal. Here, we report a discrete-modulated continuous-variable quantum key distribution system with a composable secret key rate of 18.93 Mbps against collective attacks over a 25-km fiber channel. This record-breaking rate is achieved through the probability-shaped 16 quadrature amplitude modulation-modulated protocol, which employs semidefinite programming to ensure its composable security. Furthermore, we have employed a fully digital and precise quantum signal processing technique to reduce excess noise to extremely low levels, thereby facilitating efficient broadband system operation. While ensuring low complexity and cost, our system achieves a performance advantage of over an order of magnitude compared to previous continuous-variable quantum key distribution systems, providing a promising solution for future deployment of quantum key distribution.

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Popular Summary

Realizing high secret key rates with composable security in continuous-variable quantum key distribution remains a significant hurdle for metropolitan quantum networks. We report an experimental discrete-modulated system that achieves a composable secret key rate of 18.93 Mbps over a 25 km fiber channel. We achieve this through a probability-shaped 16QAM protocol that leverages semidefinite programming for rigorous security analysis and a high-precision digital signal processing technique to minimize excess noise. Our results show that discrete modulation can outperform traditional Gaussian formats demonstration in efficiency while maintaining low system complexity and cost. This work establishes a practical and scalable pathway for deploying high-speed, secure quantum communication across metropolitan infrastructures.

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References (58)

  1. C. H. Bennett and G. Brassard, Quantum cryptography: Public key distribution and coin tossing, in Proceedings of the IEEE International Conference on Computers (IEEE, New York, 1984).
  2. 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. Opt. Photonics 12, 1012 (2020).
  3. F. Xu, X. Ma, Q. Zhang, H.-K. Lo, and J.-W. Pan, Secure quantum key distribution with realistic devices, Rev. Mod. Phys. 92, 025002 (2020).
  4. C. Portmann and R. Renner, Security in quantum cryptography, Rev. Mod. Phys. 94, 025008 (2022).
  5. 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, 011318 (2024).
  6. V. C. Usenko, A. Acín, R. Alléaume, U. L. Andersen, E. Diamanti, T. Gehring, A. A. Hajomer, F. Kanitschar, C. Pacher, S. Pirandola et al., Continuous-variable quantum communication, arXiv:2501.12801.
  7. T. C. Ralph, Continuous variable quantum cryptography, Phys. Rev. A 61, 010303(R) (1999).
  8. F. Grosshans and P. Grangier, Continuous variable quantum cryptography using coherent states, Phys. Rev. Lett. 88, 057902 (2002).
  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, 170504 (2004).
  10. 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).
  11. Z. Li, Y.-C. Zhang, and H. Guo, User-defined quantum key distribution, arXiv:1805.04249.
  12. S. Ghorai, P. Grangier, E. Diamanti, and A. Leverrier, Asymptotic security of continuous-variable quantum key distribution with a discrete modulation, Phys. Rev. X 9, 021059 (2019).
  13. J. Lin, T. Upadhyaya, and N. Lütkenhaus, Asymptotic security analysis of discrete-modulated continuous-variable quantum key distribution, Phys. Rev. X 9, 041064 (2019).
  14. A. Denys, P. Brown, and A. Leverrier, Explicit asymptotic secret key rate of continuous-variable quantum key distribution with an arbitrary modulation, Quantum 5, 540 (2021).
  15. A. Leverrier, Composable security proof for continuous-variable quantum key distribution with coherent states, Phys. Rev. Lett. 114, 070501 (2015).
  16. A. Leverrier, Security of continuous-variable quantum key distribution via a Gaussian de Finetti reduction, Phys. Rev. Lett. 118, 200501 (2017).
  17. S. Pirandola, Composable security for continuous variable quantum key distribution: Trust levels and practical key rates in wired and wireless networks, Phys. Rev. Res. 3, 043014 (2021).
  18. S. Pirandola and P. Papanastasiou, Improved composable key rates for CV-QKD, Phys. Rev. Res. 6, 023321 (2024).
  19. 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 (2013).
  20. G. Zhang, J. Y. Haw, H. Cai, F. Xu, S. Assad, J. F. Fitzsimons, X. Zhou, Y. Zhang, S. Yu, J. Wu et al., An integrated silicon photonic chip platform for continuous-variable quantum key distribution, Nat. Photonics 13, 839 (2019).
  21. 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).
  22. 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).
  23. Y. Tian, P. Wang, J. Liu, S. Du, W. Liu, Z. Lu, X. Wang, and Y. Li, Experimental demonstration of continuous-variable measurement-device-independent quantum key distribution over optical fiber, Optica 9, 492 (2022).
  24. Y. Pi, H. Wang, Y. Pan, Y. Shao, Y. Li, J. Yang, Y. Zhang, W. Huang, and B. Xu, Sub-mbps key-rate continuous-variable quantum key distribution with local local oscillator over 100-km fiber, Opt. Lett. 48, 1766 (2023).
  25. A. A. Hajomer, I. Derkach, N. Jain, H.-M. Chin, U. L. Andersen, and T. Gehring, Long-distance continuous-variable quantum key distribution over 100-km fiber with local local oscillator, Sci. Adv. 10, eadi9474 (2024).
  26. Y. Bian, Y. Pan, X. Xu, L. Zhao, Y. Li, W. Huang, L. Zhang, S. Yu, Y. Zhang, and B. Xu, Continuous-variable quantum key distribution over 28.6 km fiber with an integrated silicon photonic receiver chip, Appl. Phys. Lett. 124, 174001 (2024).
  27. P. Jouguet, S. Kunz-Jacques, E. Diamanti, and A. Leverrier, Analysis of imperfections in practical continuous-variable quantum key distribution, Phys. Rev. A 86, 032309 (2012).
  28. A. A. Hajomer, C. Bruynsteen, I. Derkach, N. Jain, A. Bomhals, S. Bastiaens, U. L. Andersen, X. Yin, and T. Gehring, Continuous-variable quantum key distribution at 10 gbaud using an integrated photonic-electronic receiver, Optica 11, 1197 (2024).
  29. H. Wang, Y. Li, Y. Pi, Y. Pan, Y. Shao, L. Ma, Y. Zhang, J. Yang, T. Zhang, W. Huang et al., Sub-gbps key rate four-state continuous-variable quantum key distribution within metropolitan area, Commun. Phys. 5, 162 (2022).
  30. Y. Pan, H. Wang, Y. Shao, Y. Pi, Y. Li, B. Liu, W. Huang, and B. Xu, Experimental demonstration of high-rate discrete-modulated continuous-variable quantum key distribution system, Opt. Lett. 47, 3307 (2022).
  31. D. Pereira, M. Almeida, M. Facão, A. N. Pinto, and N. A. Silva, Probabilistic shaped 128-APSK CV-QKD transmission system over optical fibres, Opt. Lett. 47, 3948 (2022).
  32. Y. Tian, Y. Zhang, S. Liu, P. Wang, Z. Lu, X. Wang, and Y. Li, High-performance long-distance discrete-modulation continuous-variable quantum key distribution, Opt. Lett. 48, 2953 (2023).
  33. F. Roumestan, A. Ghazisaeidi, J. Renaudier, L. T. Vidarte, A. Leverrier, E. Diamanti, and P. Grangier, Shaped constellation continuous variable quantum key distribution: Concepts, methods and experimental validation, J. Lightwave Technol. 42, 5182 (2024).
  34. Y. Pan, M. Wu, H. Wang, J. Li, Y. Shao, Y. Li, W. Huang, S. Yu, Y. Zhang, and B. Xu, Long-distance discrete-modulated continuous-variable quantum key distribution over 126.56 km of fiber, in Proceedings of the 2025 Optical Fiber Communications Conference and Exhibition (OFC) (IEEE, New York, 2025) pp. 1–3.
  35. Y. Bian, L. Fan, X. Xu, L. Zhao, M. Wu, S. Yu, and Y. Zhang, 40-km mbps discrete-modulated continuous variable quantum key distribution with constellation shaping pre-optimization, in Proceedings of the 2025 Optical Fiber Communications Conference and Exhibition (OFC) (IEEE, New York, 2025) pp. 1–3.
  36. F. Kanitschar, I. George, J. Lin, T. Upadhyaya, and N. Lütkenhaus, Finite-size security for discrete-modulated continuous-variable quantum key distribution protocols, PRX Quantum 4, 040306 (2023).
  37. S. Bäuml, C. Pascual-García, V. Wright, O. Fawzi, and A. Acín, Security of discrete-modulated continuous-variable quantum key distribution, Quantum 8, 1418 (2024).
  38. J. Lin and N. Lütkenhaus, Trusted detector noise analysis for discrete modulation schemes of continuous-variable quantum key distribution, Phys. Rev. Appl. 14, 064030 (2020).
  39. T. Upadhyaya, T. van Himbeeck, J. Lin, and N. Lütkenhaus, Dimension reduction in quantum key distribution for continuous-and discrete-variable protocols, PRX Quantum 2, 020325 (2021).
  40. P. J. Coles, E. M. Metodiev, and N. Lütkenhaus, Numerical approach for unstructured quantum key distribution, Nat. Commun. 7, 11712 (2016).
  41. A. Winick, N. Lütkenhaus, and P. J. Coles, Reliable numerical key rates for quantum key distribution, Quantum 2, 77 (2018).
  42. Y. Pan, Y. Bian, L. Ma, H. Wang, J. Dou, Y. Shao, Y. Pi, T. Ye, J. Yang, Y. Li et al., High-rate quantum access network using coherent states, in Proceedings of the 2024 Optical Fiber Communications Conference and Exhibition (OFC) (IEEE, New York, 2024) pp. 1–3.
  43. Z. Chen, X. Wang, S. Yu, Z. Li, and H. Guo, Continuous-mode quantum key distribution with digital signal processing, npj Quantum Inf. 9, 28 (2023).
  44. L. Fan, Z. Li, S. Liu, X. Xu, T. Zhang, J. Mi, D. Wang, D. Zhang, H. Li, S. Yu, and Y. Zhang, Practical continuous-variable quantum key distribution using dynamic digital signal processing: Security proof and experimental demonstration, arXiv:2602.05206 (2026).
  45. A. A. Hajomer, F. Kanitschar, N. Jain, M. Hentschel, R. Zhang, N. Lütkenhaus, U. L. Andersen, C. Pacher, and T. Gehring, Experimental composable key distribution using discrete-modulated continuous variable quantum cryptography, Light Sci. Appl. 14, 255 (2025).
  46. N. T. Islam, C. C. W. Lim, C. Cahall, J. Kim, and D. J. Gauthier, Provably secure and high-rate quantum key distribution with time-bin qudits, Sci. Adv. 3, e1701491 (2017).
  47. Z. Yuan, A. Plews, R. Takahashi, K. Doi, W. Tam, A. Sharpe, A. Dixon, E. Lavelle, J. Dynes, A. Murakami et al., 10-mb/s quantum key distribution, J. Lightwave Technol. 36, 3427 (2018).
  48. W. Li, L. Zhang, H. Tan, Y. Lu, S.-K. Liao, J. Huang, H. Li, Z. Wang, H.-K. Mao, B. Yan et al., High-rate quantum key distribution exceeding 110 mb s–1, Nat. Photonics 17, 416 (2023).
  49. F. Dupuis, O. Fawzi, and R. Renner, Entropy accumulation, Commun. Math. Phys. 379, 867 (2020).
  50. C. Pascual-García, S. Bäuml, M. Araújo, R. Liss, and A. Acín, Improved finite-size key rates for discrete-modulated continuous-variable quantum key distribution under coherent attacks, Phys. Rev. A 111, 022610 (2025).
  51. T. Metger, O. Fawzi, D. Sutter, and R. Renner, Generalised entropy accumulation, Commun. Math. Phys. 405, 261 (2024).
  52. A. Arqand and E. Y.-Z. Tan, Marginal-constrained entropy accumulation theorem, arXiv:2502.02563.
  53. M. Navarro, A. G. Lorente, P. V. Parellada, C. Pascual-García, and M. Araújo, Finite-size quantum key distribution rates from rényi entropies using conic optimization, arXiv:2511.10584.
  54. H. Hu, J. Im, J. Lin, N. Lütkenhaus, and H. Wolkowicz, Robust interior point method for quantum key distribution rate computation, Quantum 6, 792 (2022).
  55. M. Karimi and L. Tuncel, Efficient implementation of interior-point methods for quantum relative entropy, INFORMS J. Comput. 37, 3 (2025).
  56. G. Koßmann and R. Schwonnek, Optimising the relative entropy under semi definite constraints–a new tool for estimating key rates in qkd, npj Quantum Inf. 12, 23 (2026).
  57. A. Leverrier, Information reconciliation for discretely-modulated continuous-variable quantum key distribution, arXiv:2310.17548.
  58. T. Upadhyaya, Tools for the security analysis of quantum key distribution in infinite dimensions, Master’s thesis, University of Waterloo, 2021.

Outline

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Phys. Rev. X 16, 021039– Published 20 May, 2026
  • Received 14 March 2025
  • Revised 14 February 2026
  • Accepted 23 April 2026
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