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

Long-range photonic device-independent quantum key distribution using spontaneous parametric down-conversion sources and linear optics

Morteza Moradi1, Maryam Afsary1, Piotr Mironowicz2,3, Enky Oudot4,5, and Magdalena Stobińska-Moretto6,*

  • *Contact author: magdalena.stobinska@gmail.com

Phys. Rev. Research 8, 023290 – Published 12 June, 2026

DOI: https://doi.org/10.1103/ycd9-nc6q

Abstract

We address the question of the implementation of long-distance device-independent quantum key distribution (DI QKD) by proposing two experimentally viable schemes. Those schemes use only spontaneous parametric down-conversion sources and linear optics. They achieve favorable key rate scaling proportional to the square root of channel transmittance ηt, matching the twin-field protocol advantage. We demonstrate positive asymptotic key rates at detector efficiencies as low as 80%, bringing DI QKD within the reach of current superconducting detector technology. Our security analysis employs the entropy accumulation theorem to establish rigorous finite-size bounds, achieving finite-key rates at a detector efficiency of 90%. This work represents a critical milestone toward device-independent security in quantum communication networks, providing experimentalists with practical implementation pathways while maintaining the strongest possible security guarantees against quantum adversaries.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (48)

  1. V. Zapatero et al., Advances in device-independent quantum key distribution, npj Quantum Inf. 9, 10 (2023).
  2. I. W. Primaatmaja et al., Security of device-independent quantum key distribution protocols: A review, Quantum 7, 932 (2023).
  3. I. Gerhardt, Q. Liu, A. Lamas-Linares, J. Skaar, C. Kurtsiefer, and V. Makarov, Full-field implementation of a perfect eavesdropper on a quantum cryptography system, Nat. Commun. 2, 349 (2011).
  4. L. Lydersen, C. Wiechers, C. Wittmann, D. Elser, J. Skaar, and V. Makarov, Hacking commercial quantum cryptography systems by tailored bright illumination, Nat. Photon. 4, 686 (2010).
  5. Y. Zhao, C.-H. F. Fung, B. Qi, C. Chen, and H.-K. Lo, Quantum hacking: Experimental demonstration of time-shift attack against practical quantum-key-distribution systems, Phys. Rev. A 78, 042333 (2008).
  6. H. Weier, H. Krauss, M. Rau, M. Fürst, S. Nauerth, and H. Weinfurter, Quantum eavesdropping without interception: An attack exploiting the dead time of single-photon detectors, New J. Phys. 13, 073024 (2011).
  7. M. Giustina, A. Mech, S. Ramelow, B. Wittmann, J. Kofler, J. Beyer, A. Lita, B. Calkins, T. Gerrits, S. W. Nam, R. Ursin, and A. Zeilinger, Bell violation using entangled photons without the fair-sampling assumption, Nature (London) 497, 227 (2013).
  8. T. McDermott, M. Moradi, A. Mikos-Nuszkiewicz, and M. Stobińska, Eberhard limit for photon-counting Bell tests and its utility in quantum key distribution, arXiv:2211.15033.
  9. S. Pirandola et al., Advances in quantum cryptography, Adv. Opt. Photon. 12, 1012 (2020).
  10. D. P. Nadlinger et al., Experimental quantum key distribution certified by Bell’s theorem, Nature (London) 607, 682 (2022).
  11. W. Zhang et al., A device-independent quantum key distribution system for distant users, Nature (London) 607, 687 (2022).
  12. W.-Z. Liu, Y.-Z. Zhang, Y.-Z. Zhen, M.-H. Li, Y. Liu, J. Fan, F. Xu, Q. Zhang, and J.-W. Pan, Toward a photonic demonstration of device-independent quantum key distribution, Phys. Rev. Lett. 129, 050502 (2022).
  13. A. Sadhu, M. A. Somayajula, K. Horodecki, and S. Das, Practical limitations on robustness and scalability of quantum Internet, arXiv:2308.12739.
  14. 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).
  15. A. Steffinlongo, M. Navarro, M. Cenni, X. Valcarce, A. Acín, and E. Oudot, Long-distance device-independent quantum key distribution using single-photon entanglement, arXiv:2409.17075.
  16. P. Caspar, E. Verbanis, E. Oudot, N. Maring, F. Samara, M. Caloz, M. Perrenoud, P. Sekatski, A. Martin, N. Sangouard, H. Zbinden, and R. T. Thew, Heralded distribution of single-photon path entanglement, Phys. Rev. Lett. 125, 110506 (2020).
  17. M. E. Mycroft, T. McDermott, A. Buraczewski, and M. Stobińska, Proposal for the distribution of multiphoton entanglement with optimal rate-distance scaling, Phys. Rev. A 107, 012607 (2023).
  18. P. Brown, H. Fawzi, and O. Fawzi, Device-independent lower bounds on the conditional von Neumann entropy, Quantum 8, 1445 (2024).
  19. F. Dupuis and O. Fawzi, Entropy accumulation with finite-size corrections, IEEE Trans. Inf. Theory 65, 7596 (2019).
  20. F. Dupuis, O. Fawzi, and R. Renner, Entropy accumulation, Commun. Math. Phys. 379, 867 (2020).
  21. F. Kaneda, K. Garay-Palmett, A. B. U’Ren, and P. G. Kwiat, Heralded single-photon source utilizing highly nondegenerate, spectrally factorable spontaneous parametric downconversion, Opt. Express 24, 10733 (2016).
  22. V. C. Vivoli, T. Barnea, C. Galland, and N. Sangouard, Proposal for an optomechanical Bell test, Phys. Rev. Lett. 116, 070405 (2016).
  23. A. Acín, N. Brunner, N. Gisin, S. Massar, S. Pironio, and V. Scarani, Device-independent security of quantum cryptography against collective attacks, Phys. Rev. Lett. 98, 230501 (2007).
  24. J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, Proposed experiment to test local hidden-variable theories, Phys. Rev. Lett. 23, 880 (1969).
  25. K. Banaszek and K. Wódkiewicz, Testing quantum nonlocality in phase space, Phys. Rev. Lett. 82, 2009 (1999).
  26. E. M. González-Ruiz, J. Rivera-Dean, M. F. B. Cenni, A. S. Sørensen, A. Acín, and E. Oudot, Device-independent quantum key distribution with realistic single-photon source implementations, Opt. Express 32, 13181 (2024).
  27. S. Pironio, A. Acín, N. Brunner, N. Gisin, S. Massar, and V. Scarani, Device-independent quantum key distribution secure against collective attacks, New J. Phys. 11, 045021 (2009).
  28. I. Devetak and A. Winter, Distillation of secret key and entanglement from quantum states, Proc. R. Soc. A: Math. Phys. Eng. Sci. 461, 207 (2005).
  29. M. Ho, P. Sekatski, E. Y. Z. Tan, R. Renner, J. D. Bancal, and N. Sangouard, Noisy preprocessing facilitates a photonic realization of device-independent quantum key distribution, Phys. Rev. Lett. 124, 230502 (2020).
  30. M. Navascués, S. Pironio, and A. Acín, A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations, New J. Phys. 10, 073013 (2008).
  31. F. Xu, Y.-Z. Zhang, Q. Zhang, and J.-W. Pan, Device-independent quantum key distribution with random postselection, Phys. Rev. Lett. 128, 110506 (2022).
  32. M. Masini, S. Pironio, and E. Woodhead, Simple and practical DIQKD security analysis via BB84-type uncertainty relations and Pauli correlation constraints, Quantum 6, 843 (2022).
  33. W. Dai, T. Krovetz, VHASH security, Cryptology ePrint Archive (2007), available at: https://ia.cr/2007/338.
  34. A. J. Stolk et al., Metropolitan-scale heralded entanglement of solid-state qubits, Sci. Adv. 10, eadp6442 (2024).
  35. S.-R. Zhao, S. Zhao, H.-H. Dong, W.-Z. Liu, J.-L. Chen, K. Chen, Q. Zhang, and J.-W. Pan, Loophole-free test of local realism via Hardy’s violation, Phys. Rev. Lett. 133, 060201 (2024).
  36. B.-W. Lu et al., Device-independent quantum key distribution over 100 km with single atoms, Science 391, 592 (2026).
  37. Y. K. Alwehaibi, E. Mer, G. J. Machado, S. Yu, I. A. Walmsley, and R. B. Patel, A tractable protocol for detection-loophole-free Bell tests over long distances, Phys. Rev. Res. 7, 043198 (2025).
  38. M. Ishihara, A. Brendan, W. Roga, U. L. Andersen, and M. Takeoka, Long-distance device-independent quantum key distribution with standard optics tools, Opt. Quantum 3, 535 (2025).
  39. P. Wittek, Algorithm 950: Ncpol2sdpa—Sparse semidefinite programming relaxations for polynomial optimization problems of noncommuting variables, ACM Trans. Math. Softw. 41, 1 (2015).
  40. MOSEK ApS, The MOSEK Python Fusion API manual, Version 11.0 (2025), available at: https://docs.mosek.com/11.0/pythonfusion/index.html.
  41. P. Mironowicz and M. Bourennane, Finite-size security analysis for quantum protocols: A Python framework using the entropy accumulation theorem with graphical interface, arXiv:2506.18888.
  42. G. S. Thekkadath, M. E. Mycroft, B. A. Bell, C. G. Wade, A. Eckstein, D. S. Phillips, R. B. Patel, A. Buraczewski, A. E. Lita, T. Gerrits, S. W. Nam, M. Stobińska, A. I. Lvovsky, and I. A. Walmsley, Quantum-enhanced interferometry with large heralded photon-number states, npj Quantum Inf. 6, 89 (2020).
  43. M. Stobińska, A. Buraczewski, M. Moore, W. R. Clements, J. J. Renema, S. W. Nam, A. Lita, W. S. Kolthammer, A. Eckstein, and I. A. Walmsley, Quantum interference enables constant-time quantum information processing, Sci. Adv. 5, eaau9674 (2019).
  44. P. Mironowicz, Semi-definite programming and quantum information, J. Phys. A: Math. Theor. 57, 163002 (2024).
  45. O. Nieto-Silleras, S. Pironio, and J. Silman, Using complete measurement statistics for optimal device-independent randomness evaluation, New J. Phys. 16, 013035 (2014).
  46. J. D. Bancal, L. Sheridan, and V. Scarani, More randomness from the same data, New J. Phys. 16, 033011 (2014).
  47. A. M. Brańczyk, Hong–Ou–Mandel interference, Can. J. Phys. 102, 411 (2024).
  48. A. M. Brańczyk, T. C. Ralph, W. Helwig, and C. Silberhorn, Optimized generation of heralded Fock states using parametric down-conversion, New J. Phys. 12, 063001 (2010).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation