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

High-Dimensional Quantum Key Distribution via Full Core-Mode Encoding over Deployed Multicore Fibers

G. H. dos Santos1,2,*, K. B. Sawada1,2,*, N. Villalba1,2, C. Jara1,2, N. Guerrero1,2, C. Melo3, M. H. Magiotto4, D. Martinez5,6, G. B. Xavier7 et al.

J. Cariñe8, G. Saavedra3, E. S. Gómez1, S. P. Walborn1,2, and G. Lima1,2,†

  • *These authors equally contributed to this work.
  • †Contact author: glima@udec.cl

PRX Quantum 7, 043012 – Published 19 October, 2026

DOI: https://doi.org/10.1103/y779-t6ry

Abstract

Quantum key distribution (QKD) provides information-theoretic security rooted in quantum physics, while high-dimensional (HD) encoding increases both noise tolerance and secret-key yield. Multicore fibers (MCFs), a leading platform for next-generation telecom networks, are a natural substrate for HD-QKD. Field demonstrations over deployed MCFs have so far relied on a hybrid qudit encoding strategy that combines two path (core modes) with the time-bin photonic degree of freedom, rather than exploiting the full set of available core modes. Although practical, this current approach incurs intrinsic efficiency penalties that grow with dimension. Encoding a qudit in the full set of core modes removes these penalties, but it requires the coherent control of all cores at once and has so far been restricted to laboratory settings. Here we implement a four-dimensional (d=4) QKD protocol that directly exploits the full set of core modes of a four-core MCF, operating over an installed MCF network across the Universidad de Concepción campus under continuous environmental perturbations. We further benchmark the scheme using superconducting nanowire detectors at 10 dB channel loss, achieving a composable finite-key rate of R=6.19×10−3  bits/pulse, the highest per-pulse rate reported to date for deployed HD-QKD at comparable loss. This result establishes core-mode encoding as a viable architecture for realistic, high-rate quantum-secure communications.

View figure in article

Physics Subject Headings (PhySH)

Popular Summary

Article Text

References (39)

  1. C. H. Bennett and G. Brassard, Quantum cryptography: Public key distribution and coin tossing, in Proceedings of IEEE International Conference on Computers, Systems and Signal Processing (IEEE, New York, 1984), pp. 175–179.
  2. C. H. Bennett and G. Brassard, Quantum cryptography: Public key distribution and coin tossing, Theor. Comput. Sci. 560, 7 (2014).
  3. S. Pirandola, U. L. Andersen, L. Banchi, M. Berta, D. Bunandar, R. Colbeck, D. Englund, T. Gehring, C. Lupo, C. Ottaviani, J. L. Pereira, M. Razavi, J. S. Shaari, M. Tomamichel, V. C. Usenko, G. Vallone, P. Villoresi, and P. Wallden, Advances in quantum cryptography, Adv. Opt. Photonics 12, 1012 (2020).
  4. 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).
  5. P. W. Shor, Algorithms for quantum computation: Discrete logarithms and factoring, in Proceedings of the 35th Annual Symposium on Foundations of Computer Science (IEEE Computer Society Press, Los Alamitos, CA, 1994), pp. 124–134.
  6. P. W. Shor, Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer, SIAM J. Comput. 26, 1484 (1997).
  7. N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, Security of quantum key distribution using d-level systems, Phys. Rev. Lett. 88, 127902 (2002).
  8. L. Sheridan and V. Scarani, Security proof for quantum key distribution using qudit systems, Phys. Rev. A 82, 030301(R) (2010).
  9. H. Bechmann-Pasquinucci and W. Tittel, Quantum cryptography using larger alphabets, Phys. Rev. A 61, 062308 (2000).
  10. D. Cozzolino, B. Da Lio, D. Bacco, and L. K. Oxenløwe, High-dimensional quantum communication: Benefits, progress, and future challenges, Adv. Quantum Technol. 2, 1900038 (2019).
  11. D. Bruß and C. Macchiavello, Optimal eavesdropping in cryptography with three-dimensional quantum states, Phys. Rev. Lett. 88, 127901 (2002).
  12. G. B. Xavier and G. Lima, Quantum information processing with space-division multiplexing optical fibres, Commun. Phys. 3, 9 (2020).
  13. D. J. Richardson, Filling the light pipe, Science 330, 327 (2010).
  14. D. J. Richardson, J. M. Fini, and L. E. Nelson, Space-division multiplexing in optical fibres, Nat. Photonics 7, 354 (2013).
  15. I. Morita, K. Igarashi, H. Takahashi, T. Tsuritani, and M. Suzuki, Trans-oceanic class ultra-long-haul transmission using multi-core fiber, Opt. Express 22, 31761 (2014).
  16. D. Soma, S. Beppu, Y. Wakayama, K. Igarashi, T. Tsuritani, I. Morita, and M. Suzuki, 10.16-peta-B/s dense SDM/WDM transmission over 6-mode 19-core fiber across the C+L band, J. Lightwave Technol. 36, 1375 (2018).
  17. H. Takeshita, K. Nakamura, Y. Matsuo, T. Inoue, D. Masuda, T. Hiwatashi, K. Hosokawa, Y. Inada, and E. L. T. de Gabory, Demonstration of uncoupled 4-core multicore fiber in submarine cable prototype with integrated multicore EDFA, J. Lightwave Technol. 41, 980 (2023).
  18. Q. Wu et al., Integration of quantum key distribution and high-throughput classical communications in field-deployed multi-core fibers, Light:Sci. Appl. 14, 274 (2025).
  19. C. Melo, M. Reyes F., D. Arroyo, E. S. Gómez, S. P. Walborn, G. Lima, M. Figueroa, J. Cariñe, and G. Saavedra, All-fiber architecture for high speed core-selective switch for multicore fibers, Commun. Eng. 4, 77 (2025).
  20. Y. Chen et al., High-capacity optical communication relayed by multi-core amplifier on deployed submarine seven-core fiber cable, Commun. Eng. 5, 108 (2026).
  21. G. Cañas, N. Vera, J. Cariñe, P. González, J. Cardenas, P. W. R. Connolly, A. Przysiezna, E. S. Gómez, M. Figueroa, G. Vallone, P. Villoresi, T. F. da Silva, G. B. Xavier, and G. Lima, High-dimensional decoy-state quantum key distribution over multicore telecommunication fibers, Phys. Rev. A 96, 022317 (2017).
  22. Y. Ding, D. Bacco, K. Dalgaard, X. Cai, X. Zhou, K. Rottwitt, and L. K. Oxenløwe, High-dimensional quantum key distribution based on multicore fiber using silicon photonic integrated circuits, npj Quantum Inf. 3, 25 (2017).
  23. B. Da Lio, L. K. Oxenlowe, D. Bacco, D. Cozzolino, N. Biagi, T. N. Arge, E. Larsen, K. Rottwitt, Y. Ding, and A. Zavatta, Stable transmission of high-dimensional quantum states over a 2-km multicore fiber, IEEE J. Sel. Top. Quantum Electron. 26, 1 (2020).
  24. D. Bacco, N. Biagi, I. Vagniluca, T. Hayashi, A. Mecozzi, C. Antonelli, L. K. Oxenløwe, and A. Zavatta, Characterization and stability measurement of deployed multicore fibers for quantum applications, Photonics Res. 9, 1992 (2021).
  25. J. Cariñe, G. Cañas, P. Skrzypczyk, I. Šupić, N. Guerrero, T. Garcia, L. Pereira, M. A. S. Prosser, G. B. Xavier, A. Delgado, S. P. Walborn, D. Cavalcanti, and G. Lima, Multi-core fiber integrated multi-port beam splitters for quantum information processing, Optica 7, 542 (2020).
  26. M. Zahidy, D. Ribezzo, C. De Lazzari, I. Vagniluca, N. Biagi, R. Müller, T. Occhipinti, L. K. Oxenløwe, M. Galili, T. Hayashi, D. Cassioli, A. Mecozzi, C. Antonelli, A. Zavatta, and D. Bacco, Practical high-dimensional quantum key distribution protocol over deployed multicore fiber, Nat. Commun. 15, 1651 (2024).
  27. A. Alarcón, J. Argillander, G. Lima, and G. B. Xavier, Few-mode-fiber technology fine-tunes losses in quantum communication systems, Phys. Rev. Appl. 16, 034018 (2021).
  28. 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).
  29. H.-K. Lo, X. Ma, and K. Chen, Decoy state quantum key distribution, Phys. Rev. Lett. 94, 230504 (2005).
  30. Z. Cao, Z. Zhang, H.-K. Lo, and X. Ma, Discrete-phase-randomized coherent state source and its application in quantum key distribution, New J. Phys. 17, 053014 (2015).
  31. D. Rusca, A. Boaron, M. Curty, A. Martin, and H. Zbinden, Security proof for a simplified Bennett-Brassard 1984 quantum-key-distribution protocol, Phys. Rev. A 98, 052336 (2018).
  32. Z. Zhang, Q. Zhao, M. Razavi, and X. Ma, Improved key-rate bounds for practical decoy-state quantum-key-distribution systems, Phys. Rev. A 95, 012333 (2017).
  33. C. C. W. Lim, M. Curty, N. Walenta, F. Xu, and H. Zbinden, Concise security bounds for practical decoy-state quantum key distribution, Phys. Rev. A 89, 022307 (2014).
  34. T. Hayashi, T. Taru, O. Shimakawa, T. Sasaki, and E. Sasaoka, Design and fabrication of ultra-low crosstalk and low-loss multi-core fiber, Opt. Express 19, 16576 (2011).
  35. D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, Measurement of qubits, Phys. Rev. A 64, 052312 (2001).
  36. M. S. Kaznady and D. F. V. James, Numerical strategies for quantum tomography: Alternatives to full optimization, Phys. Rev. A 79, 022109 (2009).
  37. H. Abarzúa, C. Melo, S. E. Restrepo, S. Vergara, D. Sbarbaro, G. Cañas, G. Lima, G. Saavedra, and J. Cariñe, Adaptive-step perturb-and-observe algorithm for multidimensional phase noise stabilization in fiber-based multi-arm Mach–Zehnder interferometers, Algorithms 17, 534 (2024).
  38. W. Li, L. Zhang, H. Tan, Y. Lu, S.-K. Liao, J. Huang, H. Li, Z. Wang, H.-K. Mao, B. Yan, Q. Li, Y. Liu, Q. Zhang, C.-Z. Peng, L. You, F. Xu, and J.-W. Pan, High-rate quantum key distribution exceeding 110  Mbs−1, Nat. Photonics 17, 416 (2023).
  39. E. S. Gómez, S. Gómez, I. Machuca, A. Cabello, S. Pádua, S. P. Walborn, and G. Lima, Multidimensional entanglement generation with multicore optical fibers, Phys. Rev. Appl. 15, 034024 (2021).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation