- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Applied

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

Multiuser quantum key distribution using quotient graph states derived from continuous-variable dual-rail cluster states

Akash nag Oruganti*

  • *Contact author: akash.nag.10@gmail.com
PDF

Phys. Rev. Applied 24, 054049 – Published 17 November, 2025

DOI: https://doi.org/10.1103/vsqj-ndkn

Abstract

Multipartite entangled states are essential for multiuser quantum cryptography. While large-scale continuous-variable (CV) cluster states, particularly the dual-rail cluster state, have been well studied in measurement-based quantum computation, their cryptographic potential remains underexplored. Here, we propose a three-user conference key protocol using a CV dual-rail cluster state. By applying a node-coloring scheme to the infinite dual-rail graph, we create a six-mode pure graph state ideal for cryptographic tasks. Our results demonstrate near-GHZ (Greenberger-Horne-Zeilinger) performance for quantum conference key agreement (QCKA). Crucially, our protocol uniquely enables bipartite keys post-QCKA, which GHZ states cannot provide. It also surpasses two-mode squeezed vacuum states in generating bipartite keys within downstream-access networks. Considering finite-size effects and impure squeezed states, our scheme remains robust despite experimental imperfections. We also introduce an enhanced method to more accurately estimate bipartite key generation capacity in quantum networks, paving the way for practical multiuser quantum cryptography.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (41)

  1. J. Wang, G.-B. Xu, and D.-H. Jiang, Quantum voting scheme with Greenberger–Horne–Zeilinger states, Int. J. Theor. Phys. 59, 2599 (2020).
  2. Y. Guo, Y. Feng, and G. Zeng, Quantum anonymous voting with unweighted continuous-variable graph states, Quantum Inf. Process. 15, 3327 (2016).
  3. Q. Wang, C. Yu, F. Gao, H. Qi, and Q. Wen, Self-tallying quantum anonymous voting, Phys. Rev. A 94, 022333 (2016).
  4. H.-K. Lau and C. Weedbrook, Quantum secret sharing with continuous-variable cluster states, Phys. Rev. A 88, 042313 (2013).
  5. Y. Wu, R. Cai, G. He, and J. Zhang, Quantum secret sharing with continuous variable graph state, Quantum Inf. Process. 13, 1085 (2014).
  6. A. Karlsson, M. Koashi, and N. Imoto, Quantum entanglement for secret sharing and secret splitting, Phys. Rev. A 59, 162 (1999).
  7. D. Pan, G.-L. Long, L. Yin, Y.-B. Sheng, D. Ruan, S. X. Ng, J. Lu, and L. Hanzo, The evolution of quantum secure direct communication: On the road to the Qinternet, IEEE Commun. Surv. Tutorials 26, 1898 (2024).
  8. C. Wang, F. G. Deng, and G. L. Long, Multi-step quantum secure direct communication using multi-particle Greenberger–Horne–Zeilinger state, Opt. Commun. 253, 15 (2005).
  9. G. Murta, F. Grasselli, H. Kampermann, and D. Bruß, Quantum conference key agreement: A review, Adv. Quantum Technol. 3, 2000025 (2020).
  10. W. Zhao, R. Shi, Y. Feng, and X. Ruan, Conference key agreement based on continuous-variable quantum key distribution, Laser Phys. Lett. 18, 075205 (2021).
  11. N. C. Menicucci, P. van Loock, M. Gu, C. Weedbrook, T. C. Ralph, and M. A. Nielsen, Universal quantum computation with continuous-variable cluster states, Phys. Rev. Lett. 97, 110501 (2006).
  12. N. C. Menicucci, Fault-tolerant measurement-based quantum computing with continuous-variable cluster states, Phys. Rev. Lett. 112, 120504 (2014).
  13. M. V. Larsen, C. Chamberland, K. Noh, J. S. Neergaard-Nielsen, and U. L. Andersen, Fault-tolerant continuous-variable measurement-based quantum computation architecture, PRX Quantum 2, 030325 (2021).
  14. R. Raussendorf and H. J. Briegel, A one-way quantum computer, Phys. Rev. Lett. 86, 5188 (2001).
  15. R. Raussendorf, D. E. Browne, and H. J. Briegel, Measurement-based quantum computation on cluster states, Phys. Rev. A 68, 022312 (2003).
  16. N. C. Menicucci, X. Ma, and T. C. Ralph, Arbitrarily large continuous-variable cluster states from a single quantum nondemolition gate, Phys. Rev. Lett. 104, 250503 (2010).
  17. N. C. Menicucci, Temporal-mode continuous-variable cluster states using linear optics, Phys. Rev. A 83, 062314 (2011).
  18. S. Yokoyama, R. Ukai, S. C. Armstrong, C. Sornphiphatphong, T. Kaji, S. Suzuki, J.-i. Yoshikawa, H. Yonezawa, N. C. Menicucci, and A. Furusawa, Ultra-large-scale continuous-variable cluster states multiplexed in the time domain, Nat. Photonics 7, 982 (2013).
  19. M. V. Larsen, X. Guo, C. R. Breum, J. S. Neergaard-Nielsen, and U. L. Andersen, Deterministic generation of a two-dimensional cluster state, Science 366, 369 (2019).
  20. N. C. Menicucci, S. T. Flammia, H. Zaidi, and O. Pfister, Ultracompact generation of continuous-variable cluster states, Phys. Rev. A 76, 010302(R) (2007).
  21. N. C. Menicucci, S. T. Flammia, and O. Pfister, One-way quantum computing in the optical frequency comb, Phys. Rev. Lett. 101, 130501 (2008).
  22. M. Chen, N. C. Menicucci, and O. Pfister, Experimental realization of multipartite entanglement of 60 modes of a quantum optical frequency comb, Phys. Rev. Lett. 112, 120505 (2014).
  23. J. Roslund, R. Medeiros de Araújo, S. Jiang, C. Fabre, and N. Treps, Wavelength-multiplexed quantum networks with ultrafast frequency combs, Nat. Photonics 8, 109 (2014).
  24. A. Pickston, J. Ho, A. Ulibarrena, F. Grasselli, M. Proietti, C. L. Morrison, P. Barrow, F. Graffitti, and A. Fedrizzi, Conference key agreement in a quantum network, npj Quantum Inf. 9, 82 (2023).
  25. G. Adesso, A. Serafini, and F. Illuminati, Multipartite entanglement in three-mode Gaussian states of continuous-variable systems: Quantification, sharing structure, and decoherence, Phys. Rev. A 73, 032345 (2006).
  26. C. Godsil and G. Royle, Algebraic Graph Theory, Graduate Texts in Mathematics, Vol. 207 (Springer, New York, 2001).
  27. R. Band, O. Parzanchevski, and G. Ben-Shach, The isospectral fruits of representation theory: Quantum graphs and drums, J. Phys. A: Math. Theor. 42, 175202 (2009).
  28. G. Mutlu, On the quotient quantum graph with respect to the regular representation, Commun. Pure Appl. Anal. 20, 885 (2021).
  29. H. Krovi and T. A. Brun, Quantum walks on quotient graphs, Phys. Rev. A 75, 062332 (2007).
  30. H.-Y. Hsieh, Y.-R. Chen, H.-C. Wu, H. L. Chen, J. Ning, Y.-C. Huang, C.-M. Wu, and R.-K. Lee, Extract the degradation information in squeezed states with machine learning, Phys. Rev. Lett. 128, 073604 (2022).
  31. 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, 621 (2012).
  32. R. García-Patrón and N. J. Cerf, Unconditional optimality of Gaussian attacks against continuous-variable quantum key distribution, Phys. Rev. Lett. 97, 190503 (2006).
  33. I. Devetak and A. Winter, Relating quantum privacy and quantum coherence: An operational approach, Phys. Rev. Lett. 93, 080501 (2004).
  34. I. Devetak and A. Winter, Distillation of secret key and entanglement from quantum states, Proc. R. Soc. A 461, 207 (2005).
  35. S. Yang, Z. Yan, H. Yang, Q. Lu, Z. Lu, L. Cheng, X. Miao, and Y. Li, Information reconciliation of continuous-variables quantum key distribution: Principles, implementations and applications, EPJ Quantum Technol. 10, 40 (2023).
  36. A. Leverrier, Composable security proof for continuous-variable quantum key distribution with coherent states, Phys. Rev. Lett. 114, 070501 (2015).
  37. N. Walenta, A. Burg, D. Caselunghe, P. Trinkler, A. Poppe, T. Lunghi, C. Barreiro, M. Perrenoud, R. J. Hughes, and H. Zbinden, A fast and versatile quantum key distribution system with hardware key distillation and wavelength multiplexing, New J. Phys. 16, 013047 (2014).
  38. A. Leverrier, F. Grosshans, and P. Grangier, Finite-size analysis of a continuous-variable quantum key distribution, Phys. Rev. A 81, 062343 (2010).
  39. P. van Loock and S. L. Braunstein, Multipartite entanglement for continuous variables: A quantum teleportation network, Phys. Rev. Lett. 84, 3482 (2000).
  40. N. C. Menicucci, S. T. Flammia, and P. van Loock, Graphical calculus for Gaussian pure states, Phys. Rev. A 83, 042335 (2011).
  41. A. N. Oruganti, I. Derkach, R. Filip, and V. C. Usenko, Continuous-variable quantum key distribution with noisy squeezed states, Quantum Sci. Technol. 10, 025023 (2025).

Outline

Information

Phys. Rev. Applied 24, 054049– Published 17 November, 2025
  • Received 19 December 2024
  • Revised 6 August 2025
  • Accepted 24 September 2025
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation