- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

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

Certifying high-dimensional quantum channels

Sophie Engineer1,2,*, Suraj Goel1, Sophie Egelhaaf3, Will McCutcheon1, Vatshal Srivastav1, Saroch Leedumrongwatthanakun1,†, Sabine Wollmann1, Benjamin D. M. Jones2, Thomas Cope4,5 et al.

Nicolas Brunner3, Roope Uola3, and Mehul Malik1,‡

  • *Contact author: sophiengineer@gmail.com
  • †Present address: Division of Physical Science, Faculty of Science, Prince of Songkla University, Hat Yai, Songkhla 90110, Thailand.
  • ‡Contact author: m.malik@hw.ac.uk
PDF

Phys. Rev. Research 7, 033233 – Published 9 September, 2025

DOI: https://doi.org/10.1103/bwd5-wx7j

Abstract

The use of high-dimensional systems for quantum communication opens interesting perspectives, such as increased information capacity and noise resilience. In this context, it is crucial to certify that a given quantum channel can reliably transmit high-dimensional quantum information. Here we develop efficient methods for the characterization of high-dimensional quantum channels. We first present a notion of dimensionality of quantum channels and develop efficient certification methods for this quantity. We consider a simple prepare-and-measure setup and provide witnesses for both a fully and a partially trusted scenario. In turn, we apply these methods to a photonic experiment and certify dimensionalities up to 59 for a commercial graded-index multimode optical fiber. Moreover, we present extensive numerical simulations of the experiment, providing an accurate noise model for the fiber and exploring the potential of more sophisticated witnesses. Our work demonstrates the efficient characterization of high-dimensional quantum channels, a key ingredient for future quantum communication technologies.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (50)

  1. H. J. Kimble, The quantum internet, Nature (London) 453, 1023 (2008).
  2. F. Bouchard, F. Hufnagel, D. Koutný, A. Abbas, A. Sit, K. Heshami, R. Fickler, and E. Karimi, Quantum process tomography of a high-dimensional quantum communication channel, Quantum 3, 138 (2019).
  3. S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, Measuring the transmission matrix in optics: An approach to the study and control of light propagation in disordered media, Phys. Rev. Lett. 104, 100601 (2010).
  4. J. Carpenter, B. J. Eggleton, and J. Schröder, Observation of Eisenbud–Wgner–Smith states as principal modes in multimode fibre, Nat. Photonics 9, 751 (2015).
  5. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2010).
  6. C. Macchiavello and M. F. Sacchi, Detecting lower bounds to quantum channel capacities, Phys. Rev. Lett. 116, 140501 (2016).
  7. C. Macchiavello and M. F. Sacchi, Witnessing quantum capacities of correlated channels, Phys. Rev. A 94, 052333 (2016).
  8. C. Pfister, M. A. Rol, A. Mantri, M. Tomamichel, and S. Wehner, Capacity estimation and verification of quantum channels with arbitrarily correlated errors, Nat. Commun. 9, 27 (2018).
  9. M. F. Pusey, Verifying the quantumness of a channel with an untrusted device, J. Opt. Soc. Am. B 32, A56 (2015).
  10. D. Rosset, F. Buscemi, and Y.-C. Liang, Resource theory of quantum memories and their faithful verification with minimal assumptions, Phys. Rev. X 8, 021033 (2018).
  11. F. Graffitti, A. Pickston, P. Barrow, M. Proietti, D. Kundys, D. Rosset, M. Ringbauer, and A. Fedrizzi, Measurement-device-independent verification of quantum channels, Phys. Rev. Lett. 124, 010503 (2020).
  12. Y. Mao, Y.-Z. Zhen, H. Liu, M. Zou, Q.-J. Tang, S.-J. Zhang, J. Wang, H. Liang, W. Zhang, H. Li et al., Experimentally verified approach to nonentanglement-breaking channel certification, Phys. Rev. Lett. 124, 010502 (2020).
  13. M. Dall'Arno, S. Brandsen, and F. Buscemi, Device-independent tests of quantum channels, Proc. Royal Soc. A 473, 20160721 (2017).
  14. S. Wagner, J.-D. Bancal, N. Sangouard, and P. Sekatski, Device-independent characterization of quantum instruments, Quantum 4, 243 (2020).
  15. P. Sekatski, J.-D. Bancal, M. Ioannou, M. Afzelius, and N. Brunner, Toward the device-independent certification of a quantum memory, Phys. Rev. Lett. 131, 170802 (2023).
  16. M. Ringbauer, T. R. Bromley, M. Cianciaruso, L. Lami, W. Y. Sarah Lau, G. Adesso, A. G. White, A. Fedrizzi, and M. Piani, Certification and quantification of multilevel quantum coherence, Phys. Rev. X 8, 041007 (2018).
  17. N. H. Valencia, S. Goel, W. McCutcheon, H. Defienne, and M. Malik, Unscrambling entanglement through a complex medium, Nat. Phys. 16, 1112 (2020).
  18. F. Zhu, M. Tyler, N. H. Valencia, M. Malik, and J. Leach, Is high-dimensional photonic entanglement robust to noise? AVS Quantum Science 3, 011401 (2021).
  19. 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).
  20. Y. Zheng, C. Zhai, D. Liu, J. Mao, X. Chen, T. Dai, J. Huang, J. Bao, Z. Fu, Y. Tong, X. Zhou, Y. Yang, B. Tang, Z. Li, Y. Li, Q. Gong, H. K. Tsang, D. Dai, and J. Wang, Multichip multidimensional quantum networks with entanglement retrievability, Science 381, 221 (2023).
  21. N. H. Valencia, A. Ma, S. Goel, S. Leedumrongwatthanakun, F. Graffitti, A. Fedrizzi, W. McCutcheon, and M. Malik, A large-scale reconfigurable multiplexed quantum photonic network, arXiv:2501.07272.
  22. M. Ringbauer, M. Meth, L. Postler, R. Stricker, R. Blatt, P. Schindler, and T. Monz, A universal qudit quantum processor with trapped ions, Nat. Phys. 18, 1053 (2022).
  23. M. Mirhosseini, O. S. Magaña-Loaiza, M. N. O'Sullivan, B. Rodenburg, M. Malik, M. P. J. Lavery, M. J. Padgett, D. J. Gauthier, and R. W. Boyd, High-dimensional quantum cryptography with twisted light, New J. Phys. 17, 033033 (2015).
  24. V. Srivastav, N. H. Valencia, W. McCutcheon, S. Leedumrongwatthanakun, S. Designolle, R. Uola, N. Brunner, and M. Malik, Quick quantum steering: Overcoming loss and noise with qudits, Phys. Rev. X 12, 041023 (2022).
  25. M. Horodecki, P. W. Shor, and M. B. Ruskai, Entanglement breaking channels, Rev. Math. Phys. 15, 629 (2003).
  26. D. Chruściński and A. Kossakowski, On partially entanglement breaking channels, Open Syst. Inf. Dyn. 13, 17 (2006).
  27. J. Bavaresco, N. H. Valencia, C. Klöckl, M. Pivoluska, P. Erker, N. Friis, M. Malik, and M. Huber, Measurements in two bases are sufficient for certifying high-dimensional entanglement, Nat. Phys. 14, 1032 (2018).
  28. S. Designolle, V. Srivastav, R. Uola, N. H. Valencia, W. McCutcheon, M. Malik, and N. Brunner, Genuine high-dimensional quantum steering, Phys. Rev. Lett. 126, 200404 (2021).
  29. S. Morelli, M. Huber, and A. Tavakoli, Resource-efficient high-dimensional entanglement detection via symmetric projections, Phys. Rev. Lett. 131, 170201 (2023).
  30. W. K. Wootters and B. D. Fields, Optimal state-determination by mutually unbiased measurements, Ann. Phys. 191, 363 (1989).
  31. S. Designolle, Robust genuine high-dimensional steering with many measurements, Phys. Rev. A 105, 032430 (2022).
  32. C. de Gois, M. Plávala, R. Schwonnek, and O. Gühne, Complete hierarchy for high-dimensional steering certification, Phys. Rev. Lett. 131, 010201 (2023).
  33. More precisely, a violation of (5) implies that the effective measurements {Λ*(Ma|x)} are strongly incompatible (in the sense of being non-n-simulable [37]), which implies that both the channel Λ and the measurements {Ma|x} are high-dimensional.
  34. S. Goel, C. Conti, S. Leedumrongwatthanakun, and M. Malik, Referenceless characterization of complex media using physics-informed neural networks, Opt. Express 31, 32824 (2023).
  35. M. B. Shemirani, W. Mao, R. A. Panicker, and J. M. Kahn, Principal modes in graded-index multimode fiber in presence of spatial-and polarization-mode coupling, J. Lightwave Technol. 27, 1248 (2009).
  36. M. Berta, F. G. S. L. Brandao, M. Christandl, and S. Wehner, Entanglement cost of quantum channels, IEEE Trans. Inf. Theory 59, 6779 (2013).
  37. M. Ioannou, P. Sekatski, S. Designolle, B. D. M. Jones, R. Uola, and N. Brunner, Simulability of high-dimensional quantum measurements, Phys. Rev. Lett. 129, 190401 (2022).
  38. J. Kiukas, C. Budroni, R. Uola, and J.-P. Pellonpää, Continuous-variable steering and incompatibility via state-channel duality, Phys. Rev. A 96, 042331 (2017).
  39. N. H. Valencia, V. Srivastav, M. Pivoluska, M. Huber, N. Friis, W. McCutcheon, and M. Malik, High-dimensional pixel entanglement: efficient generation and certification, Quantum 4, 376 (2020).
  40. S. Goel, S. Leedumrongwatthanakun, N. H. Valencia, W. McCutcheon, A. Tavakoli, C. Conti, P. W. H. Pinkse, and M. Malik, Inverse design of high-dimensional quantum optical circuits in a complex medium, Nat. Phys. 20, 232 (2024).
  41. S. M. Barnett, On single-photon and classical interference, Phys. Scr. 97, 114004 (2022).
  42. M. Mounaix, H. B. de Aguiar, and S. Gigan, Temporal recompression through a scattering medium via a broadband transmission matrix, Optica 4, 1289 (2017).
  43. J. Carpenter, B. J. Eggleton, and J. Schröder, 110×110 optical mode transfer matrix inversion, Opt. Express 22, 96 (2014).
  44. R. Gutiérrez-Cuevas, A. Goetschy, Y. Bromberg, G. Pelc, E. R. Andresen, L. Bigot, Y. Quiquempois, M. Bsaibes, P. Sillard, M. Bigot et al., Characterization and exploitation of the rotational memory effect in multimode fibers, Phys. Rev. X 14, 031046 (2024).
  45. U. G. Būtaitė, H. Kupianskyi, T. Čižmár, and D. B. Phillips, How to build the “optical inverse” of a multimode fibre, Intell. Comput. 2022, 9816026 (2022).
  46. M. Plöschner, T. Tyc, and T. Čižmár, Seeing through chaos in multimode fibres, Nat. Photonics 9, 529 (2015).
  47. J. Carpenter, B. J. Eggleton, and J. Schröder, Comparison of principal modes and spatial eigenmodes in multimode optical fibre, Laser Photonics Rev. 11, 1600259 (2017).
  48. S. Fan and J. M. Kahn, Principal modes in multimode waveguides, Opt. Lett. 30, 135 (2005).
  49. M. Mounaix, D. Andreoli, H. Defienne, G. Volpe, O. Katz, S. Grésillon, and S. Gigan, Spatiotemporal coherent control of light through a multiple scattering medium with the multispectral transmission matrix, Phys. Rev. Lett. 116, 253901 (2016).
  50. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, London, 1983), Vol. 175.

Outline

Information

Phys. Rev. Research 7, 033233– Published 9 September, 2025
  • Received 1 October 2024
  • Accepted 19 May 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