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Quantum key distribution with basis-dependent detection probability

Federico Grasselli1,2,*, Giovanni Chesi3, Nathan Walk4, Hermann Kampermann1, Adam Widomski5, Maciej Ogrodnik5, Michał Karpiński5, Chiara Macchiavello3, Dagmar Bruß1 et al.

Nikolai Wyderka1,†

  • *Contact author: federico.grasselli@hhu.de
  • †Contact author: wyderka@hhu.de
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Phys. Rev. Applied 23, 044011 – Published 4 April, 2025

DOI: https://doi.org/10.1103/PhysRevApplied.23.044011

Abstract

Quantum key distribution (QKD) is a promising technology for secure communication. Nevertheless, QKD is still treated with caution in certain contexts due to potential gaps between theoretical models and actual QKD implementations. A common assumption in security proofs is that the detection probability at the receiver, for a given input state, is independent of the measurement basis, which might not always be verified and could lead to security loopholes. This paper presents a security proof for QKD protocols that does not rely on the aforementioned assumption and is thus applicable in scenarios with detection probability mismatches, even when induced by the adversary. We demonstrate, through simulations, that our proof can extract positive key rates for setups vulnerable to large detection probability mismatches. This is achieved by one monitoring whether an adversary is actively exploiting such vulnerabilities, instead of considering the worst-case scenario as in previous proofs. Our work highlights the importance of accounting for basis-dependent detection probabilities and provides a concrete solution for improving the security of practical QKD systems.

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References (58)

  1. Inside Quantum Technology, Quantum key distribution (QKD) markets: 2019–2028. https://www.insidequantumtechnology.com/product/quantum-key-distribution-qkd-markets-2019-2028 [Online].
  2. 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. Photon. 12, 1012 (2020).
  3. French Cybersecurity Agency (ANSSI), Federal Office for Information Security (BSI), Netherlands National Communications Security Agency (NLNCSA), and Swedish National Communications Security Authority (Swedish NCSA), Position paper on quantum key distribution (2024).
  4. M. Lucamarini, A. Shields, R. Alléaume, C. Chunnilall, I. P. Degiovanni, M. Gramegna, A. Hasekioglu, B. Huttner, R. Kumar, A. Lord, N. Lütkenhaus, V. Makarov, V. Martin, A. Mink, M. Peev, M. Sasaki, A. Sinclair, T. Spiller, M. Ward, C. White, and Z. Yuan, Implementation security of quantum cryptography, ETSI White Paper No. 27, (2018).
  5. V. Zapatero, A. Navarrete, and M. Curty, Implementation security in quantum key distribution, Adv. Quantum Technol. 8, 2300380 (2024).
  6. 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).
  7. P. W. Shor and J. Preskill, Simple proof of security of the BB84 quantum key distribution protocol, Phys. Rev. Lett. 85, 441 (2000).
  8. M. Tomamichel and A. Leverrier, A largely self-contained and complete security proof for quantum key distribution, Quantum 1, 14 (2017).
  9. 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).
  10. K. Tamaki, M. Curty, G. Kato, H.-K. Lo, and K. Azuma, Loss-tolerant quantum cryptography with imperfect sources, Phys. Rev. A 90, 052314 (2014).
  11. M. K. Bochkov and A. S. Trushechkin, Security of quantum key distribution with detection-efficiency mismatch in the single-photon case: Tight bounds, Phys. Rev. A 99, 032308 (2019).
  12. A. Trushechkin, Security of quantum key distribution with detection-efficiency mismatch in the multiphoton case, Quantum 6, 771 (2022).
  13. J. Nunn, L. J. Wright, C. Söller, L. Zhang, I. A. Walmsley, and B. J. Smith, Large-alphabet time-frequency entangled quantum key distribution by means of time-to-frequency conversion, Opt. Express 21, 15959 (2013).
  14. J. E. Bourassa and H.-K. Lo, Entropic uncertainty relations and the measurement range problem, with consequences for high-dimensional quantum key distribution, J. Opt. Soc. Am. B 36, B65 (2019).
  15. 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).
  16. 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).
  17. S. Sajeed, P. Chaiwongkhot, J.-P. Bourgoin, T. Jennewein, N. Lütkenhaus, and V. Makarov, Security loophole in free-space quantum key distribution due to spatial-mode detector-efficiency mismatch, Phys. Rev. A 91, 062301 (2015).
  18. A. Boaron, B. Korzh, R. Houlmann, G. Boso, D. Rusca, S. Gray, M.-J. Li, D. Nolan, A. Martin, and H. Zbinden, Simple 2.5 GHz time-bin quantum key distribution, Appl. Phys. Lett. 112, 171108 (2018).
  19. I. Vagniluca, B. Da Lio, D. Rusca, D. Cozzolino, Y. Ding, H. Zbinden, A. Zavatta, L. K. Oxenløwe, and D. Bacco, Efficient time-bin encoding for practical high-dimensional quantum key distribution, Phys. Rev. Appl. 14, 014051 (2020).
  20. 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).
  21. N. T. Islam, C. C. W. Lim, C. Cahall, B. Qi, J. Kim, and D. J. Gauthier, Scalable high-rate, high-dimensional time-bin encoding quantum key distribution, Quantum Sci. Technol. 4, 035008 (2019).
  22. J. Mower, Z. Zhang, P. Desjardins, C. Lee, J. H. Shapiro, and D. Englund, High-dimensional quantum key distribution using dispersive optics, Phys. Rev. A 87, 062322 (2013).
  23. C. Lee, D. Bunandar, Z. Zhang, G. R. Steinbrecher, P. B. Dixon, F. N. C. Wong, J. H. Shapiro, S. A. Hamilton, and D. Englund, Large-alphabet encoding for higher-rate quantum key distribution, Opt. Express 27, 17539 (2019).
  24. J. Rödiger, N. Perlot, R. Mottola, R. Elschner, C.-M. Weinert, O. Benson, and R. Freund, Numerical assessment and optimization of discrete-variable time-frequency quantum key distribution, Phys. Rev. A 95, 052312 (2017).
  25. Y. Zhang, I. B. Djordjevic, and M. A. Neifeld, Weak-coherent-state-based time-frequency quantum key distribution, J. Mod. Opt. 62, 1713 (2015).
  26. M. Leifgen, R. Elschner, N. Perlot, C. Weinert, C. Schubert, and O. Benson, Practical implementation and evaluation of a quantum-key-distribution scheme based on the time-frequency uncertainty, Phys. Rev. A 92, 042311 (2015).
  27. K.-C. Chang, M. C. Sarihan, X. Cheng, Z. Zhang, and C. W. Wong, Large-alphabet time-bin quantum key distribution and Einstein-Podolsky-Rosen steering via dispersive optics, Quantum Sci. Technol. 9, 015018 (2024).
  28. T. Moroder, M. Curty, and N. Lütkenhaus, Detector decoy quantum key distribution, New J. Phys. 11, 045008 (2009).
  29. A. Widomski, M. Ogrodnik, and M. Karpiński, Efficient detection of multidimensional single-photon time-bin superpositions, Optica 11, 926 (2024).
  30. M. Ogrodnik, A. Widomski, D. Bruß, G. Chesi, F. Grasselli, H. Kampermann, C. Macchiavello, N. Walk, N. Wyderka, and M. Karpiński, High-dimensional quantum key distribution with resource-efficient detection, arXiv:2412.16782.
  31. Federal Office for Information Security (BSI), Implementation attacks against QKD systems (2023).
  32. 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).
  33. C.-H. F. Fung, K. Tamaki, B. Qi, H.-K. Lo, and X. Ma, Security proof of quantum key distribution with detection efficiency mismatch, Quantum Inf. Comput. 9, 131 (2009).
  34. J. Ma, Y. Zhou, X. Yuan, and X. Ma, Operational interpretation of coherence in quantum key distribution, Phys. Rev. A 99, 062325 (2019).
  35. L. Lydersen and J. Skaar, Security of quantum key distribution with bit and basis dependent detector flaws, Quantum Inf. Comput. 10, 60 (2010).
  36. Y. Zhang, P. J. Coles, A. Winick, J. Lin, and N. Lütkenhaus, Security proof of practical quantum key distribution with detection-efficiency mismatch, Phys. Rev. Res. 3, 013076 (2021).
  37. H.-K. Lo, X. Ma, and K. Chen, Decoy state quantum key distribution, Phys. Rev. Lett. 94, 230504 (2005).
  38. X.-B. Wang, Beating the photon-number-splitting attack in practical quantum cryptography, Phys. Rev. Lett. 94, 230503 (2005).
  39. X. Ma, B. Qi, Y. Zhao, and H.-K. Lo, Practical decoy state for quantum key distribution, Phys. Rev. A 72, 012326 (2005).
  40. X.-S. Ma, S. Zotter, N. Tetik, A. Qarry, T. Jennewein, and A. Zeilinger, A high-speed tunable beam splitter for feed-forward photonic quantum information processing, Opt. Express 19, 22723 (2011).
  41. R. R. Carreira, J. J. Barroso, and J. E. B. Oliveira, Generalized analysis of dual-output Mach-Zehnder modulator with applications to photonic-assisted instantaneous frequency measurement, J. Lightwave Technol. 39, 7956 (2021).
  42. M. Christandl, R. König, and R. Renner, Postselection technique for quantum channels with applications to quantum cryptography, Phys. Rev. Lett. 102, 020504 (2009).
  43. S. Nahar, D. Tupkary, Y. Zhao, N. Lütkenhaus, and E. Y.-Z. Tan, Postselection technique for optical quantum key distribution with improved de Finetti reductions, PRX Quantum 5, 040315 (2024).
  44. M. Y. Niu, F. Xu, J. H. Shapiro, and F. Furrer, Finite-key analysis for time-energy high-dimensional quantum key distribution, Phys. Rev. A 94, 052323 (2016).
  45. N. Walk, J. Barrett, and J. Nunn, Composably secure time-frequency quantum key distribution, arxiv:1609.09436.
  46. I. Devetak and A. Winter, Distillation of secret key and entanglement from quantum states, Proc.: Math., Phys. Eng. Sci. 461, 207 (2005).
  47. W.-Y. Hwang, Quantum key distribution with high loss: Toward global secure communication, Phys. Rev. Lett. 91, 057901 (2003).
  48. M. Berta, M. Christandl, R. Colbeck, J. M. Renes, and R. Renner, The uncertainty principle in the presence of quantum memory, Nat. Phys. 6, 659 (2010).
  49. M. Tomamichel and R. Renner, Uncertainty relation for smooth entropies, Phys. Rev. Lett. 106, 110506 (2011).
  50. F. Furrer, T. Franz, M. Berta, A. Leverrier, V. B. Scholz, M. Tomamichel, and R. F. Werner, Continuous variable quantum key distribution: Finite-key analysis of composable security against coherent attacks, Phys. Rev. Lett. 109, 100502 (2012).
  51. F. Furrer, M. Berta, M. Tomamichel, V. B. Scholz, and M. Christandl, Position-momentum uncertainty relations in the presence of quantum memory, J. Math. Phys. 55, 122205 (2014).
  52. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information: 10th Anniversary Edition (Cambridge University Press, Cambridge, 2011).
  53. In an adversarial implementation, we cannot discard the possibility that Eve adds photons to Alice’s pulse before it reaches Bob.
  54. D. Tupkary, S. Nahar, P. Sinha, and N. Lütkenhaus, Phase error rate estimation in QKD with imperfect detectors, arXiv:2408.17349.
  55. A. Winick, N. Lütkenhaus, and P. J. Coles, Reliable numerical key rates for quantum key distribution, Quantum 2, 77 (2018).
  56. Y. Zhang and N. Lütkenhaus, Entanglement verification with detection-efficiency mismatch, Phys. Rev. A 95, 042319 (2017).
  57. S. Nahar, T. Upadhyaya, and N. Lütkenhaus, Imperfect phase randomization and generalized decoy-state quantum key distribution, Phys. Rev. Appl. 20, 064031 (2023).
  58. R. Bhatia and C. Davis, A Cauchy-Schwarz inequality for operators with applications, Linear Algebra Appl. 223–224, 119 (1995), Honoring Miroslav Fiedler and Vlastimil Ptak.

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Phys. Rev. Applied 23, 044011– Published 4 April, 2025
  • Received 9 December 2024
  • Revised 3 February 2025
  • Accepted 26 February 2025
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