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Experimental quantum key distribution certified by Bell's theorem

Nature volume 607, pages 682–686 (2022)Cite this article

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Abstract

Cryptographic key exchange protocols traditionally rely on computational conjectures such as the hardness of prime factorization1 to provide security against eavesdropping attacks. Remarkably, quantum key distribution protocols such as the Bennett–Brassard scheme2 provide information-theoretic security against such attacks, a much stronger form of security unreachable by classical means. However, quantum protocols realized so far are subject to a new class of attacks exploiting a mismatch between the quantum states or measurements implemented and their theoretical modelling, as demonstrated in numerous experiments3,4,5,6. Here we present the experimental realization of a complete quantum key distribution protocol immune to these vulnerabilities, following Ekert’s pioneering proposal7 to use entanglement to bound an adversary’s information from Bell’s theorem8. By combining theoretical developments with an improved optical fibre link generating entanglement between two trapped-ion qubits, we obtain 95,628 key bits with device-independent security9,10,11,12 from 1.5 million Bell pairs created during eight hours of run time. We take steps to ensure that information on the measurement results is inaccessible to an eavesdropper. These measurements are performed without space-like separation. Our result shows that provably secure cryptography under general assumptions is possible with real-world devices, and paves the way for further quantum information applications based on the device-independence principle.

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Fig. 1: DIQKD with trapped ions.
Fig. 2: DIQKD protocol structure.
Fig. 3: Quantum link performance.
Fig. 4: Finite-statistics key rate.

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Data availability

The datasets generated during the current study are available from D.P.N. and C.J.B. on reasonable request.

Code availability

The custom code generated during the current study is available from the corresponding authors on reasonable request.

References

  1. Rivest, R. L., Shamir, A. & Adleman, L. A method for obtaining digital signatures and public-key cryptosystems. Commun. ACM 21, 120–126 (1978).

    Article  MathSciNet  MATH  Google Scholar 

  2. Bennett, C. H. & Brassard, G. Quantum cryptography: public key distribution and coin tossing. Theor. Comput. Sci. 560, 7–11 (1984).

    Article  MathSciNet  MATH  Google Scholar 

  3. Zhao, Y., Fung, C.-H. F., Qi, B., Chen, C. & Lo, H.-K. Quantum hacking: experimental demonstration of time-shift attack against practical quantum-key-distribution systems. Phys. Rev. A 78, 042333 (2008).

    Article  ADS  Google Scholar 

  4. Lydersen, L. et al. Hacking commercial quantum cryptography systems by tailored bright illumination. Nat. Photon. 4, 686–689 (2010).

    Article  CAS  ADS  Google Scholar 

  5. Gerhardt, I. et al. Full-field implementation of a perfect eavesdropper on a quantum cryptography system. Nat. Commun. 2, 349 (2011).

  6. Weier, H. et al. Quantum eavesdropping without interception: an attack exploiting the dead time of single-photon detectors. New J. Phys. 13, 073024 (2011).

    Article  ADS  Google Scholar 

  7. Ekert, A. K. Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett. 67, 661 (1991).

    Article  MathSciNet  CAS  PubMed  MATH  ADS  Google Scholar 

  8. Bell, J. S. On the Einstein Podolsky Rosen paradox. Phys. Phys. Fiz. 1, 195–200 (1964).

    MathSciNet  Google Scholar 

  9. Mayers, D. & Yao, A. Self testing quantum apparatus. Quantum Inf. Comput. 4, 273–286 (2004).

    MathSciNet  MATH  Google Scholar 

  10. Acín, A. et al. Device-independent security of quantum cryptography against collective attacks. Phys. Rev. Lett. 98, 230501 (2007).

    Article  PubMed  ADS  Google Scholar 

  11. Vazirani, U. & Vidick, T. Fully device-independent quantum key distribution. Phys. Rev. Lett. 113, 140501 (2014).

    Article  PubMed  ADS  Google Scholar 

  12. Arnon-Friedman, R., Dupuis, F., Fawzi, O., Renner, R. & Vidick, T. Practical device-independent quantum cryptography via entropy accumulation. Nat. Commun. 9, 459 (2018).

    Article  PubMed  PubMed Central  ADS  Google Scholar 

  13. Gisin, N., Ribordy, G., Tittel, W. & Zbinden, H. Quantum cryptography. Rev. Mod. Phys. 74, 145–195 (2002).

    Article  MATH  ADS  Google Scholar 

  14. Scarani, V. et al. The security of practical quantum key distribution. Rev. Mod. Phys. 81, 1301–1350 (2009).

    Article  ADS  Google Scholar 

  15. Lo, H.-K., Curty, M. & Tamaki, K. Secure quantum key distribution. Nat. Photon. 8, 595–604 (2014).

    Article  CAS  ADS  Google Scholar 

  16. Acín, A., Gisin, N. & Masanes, L. From Bell’s theorem to secure quantum key distribution. Phys. Rev. Lett. 97, 120405 (2006).

    Article  PubMed  MATH  ADS  Google Scholar 

  17. Braunstein, S. L. & Pirandola, S. Side-channel-free quantum key distribution. Phys. Rev. Lett. 108, 130502 (2012).

    Article  PubMed  ADS  Google Scholar 

  18. Lo, H.-K., Curty, M. & Qi, B. Measurement-device-independent quantum key distribution. Phys. Rev. Lett. 108, 130503 (2012).

    Article  PubMed  ADS  Google Scholar 

  19. Rubenok, A., Slater, J. A., Chan, P., Lucio-Martinez, I. & Tittel, W. Real-world two-photon interference and proof-of-principle quantum key distribution immune to detector attacks. Phys. Rev. Lett. 111, 130501 (2013).

    Article  CAS  PubMed  ADS  Google Scholar 

  20. Ferreira da Silva, T. et al. Proof-of-principle demonstration of measurement-device-independent quantum key distribution using polarization qubits. Phys. Rev. A 88, 052303 (2013).

    Article  ADS  Google Scholar 

  21. Liu, Y. et al. Experimental measurement-device-independent quantum key distribution. Phys. Rev. Lett. 111, 130502 (2013).

    Article  PubMed  ADS  Google Scholar 

  22. Brunner, N., Cavalcanti, D., Pironio, S., Scarani, V. & Wehner, S. Bell nonlocality. Rev. Mod. Phys. 86, 419–478 (2014).

    Article  ADS  Google Scholar 

  23. Barrett, J., Hardy, L. & Kent, A. No signaling and quantum key distribution. Phys. Rev. Lett. 95, 010503 (2005).

    Article  PubMed  ADS  Google Scholar 

  24. Masanes, L. Universally composable privacy amplification from causality constraints. Phys. Rev. Lett. 102, 140501 (2009).

    Article  PubMed  ADS  Google Scholar 

  25. Reichardt, B. W., Unger, F. & Vazirani, U. Classical command of quantum systems. Nature 496, 456–460 (2013).

    Article  CAS  PubMed  ADS  Google Scholar 

  26. Ho, M. et al. Noisy preprocessing facilitates a photonic realization of device-independent quantum key distribution. Phys. Rev. Lett. 124, 230502 (2020).

    Article  CAS  PubMed  ADS  Google Scholar 

  27. Schwonnek, R. et al. Device-independent quantum key distribution with random key basis. Nat. Commun. 12, 2880 (2021).

    Article  CAS  PubMed  PubMed Central  ADS  Google Scholar 

  28. Woodhead, E., Acín, A. & Pironio, S. Device-independent quantum key distribution with asymmetric CHSH inequalities. Quantum 5, 443 (2021).

    Article  Google Scholar 

  29. Sekatski, P. et al. Device-independent quantum key distribution from generalized CHSH inequalities. Quantum 5, 444 (2021).

    Article  Google Scholar 

  30. Brown, P., Fawzi, H. & Fawzi, O. Device-independent lower bounds on the conditional von Neumann entropy. Preprint at https://arXiv.org/abs/2106.13692 (2021).

  31. Masini, M., Pironio, S. & Woodhead, E. Simple and practical DIQKD security analysis via BB84-type uncertainty relations and Pauli correlation constraints. Preprint at https://arXiv.org/abs/2107.08894 (2021).

  32. Clauser, J. F., Horne, M. A., Shimony, A. & Holt, R. A. Proposed experiment to test local hidden-variable theories. Phys. Rev. Lett. 23, 880 (1969).

    Article  MATH  ADS  Google Scholar 

  33. Dupuis, F., Fawzi, O. & Renner, R. Entropy accumulation. Commun. Math. Phys. 379, 867–913 (2020).

    Article  MathSciNet  MATH  ADS  Google Scholar 

  34. Liu, W.-Z. et al. Device-independent randomness expansion against quantum side information. Nat. Phys. 17, 448–452 (2021).

    Article  Google Scholar 

  35. Murta, G., van Dam, S. B., Ribeiro, J., Hanson, R. & Wehner, S. Towards a realization of device-independent quantum key distribution. Quantum Sci. Technol. 4, 035011 (2019).

    Article  ADS  Google Scholar 

  36. Tan, E.Y.-Z. et al. Improved DIQKD protocols with finite-size analysis. Preprint at https://arXiv.org/abs/2012.08714 (2020).

  37. Moehring, D. L. et al. Entanglement of single-atom quantum bits at a distance. Nature 449, 68–71 (2007).

    Article  CAS  PubMed  ADS  Google Scholar 

  38. Stephenson, L. J. et al. High-rate, high-fidelity entanglement of qubits across an elementary quantum network. Phys. Rev. Lett. 124, 110501 (2020).

    Article  CAS  PubMed  ADS  Google Scholar 

  39. Maunz, P. et al. Heralded quantum gate between remote quantum memories. Phys. Rev. Lett. 102, 250502 (2009).

    Article  CAS  PubMed  ADS  Google Scholar 

  40. Lettner, M. et al. Remote entanglement between a single atom and a Bose-Einstein condensate. Phys. Rev. Lett. 106, 210503 (2011).

    Article  CAS  PubMed  ADS  Google Scholar 

  41. Ritter, S. et al. An elementary quantum network of single atoms in optical cavities. Nature 484, 195–200 (2012).

    Article  CAS  PubMed  ADS  Google Scholar 

  42. Hensen, B. et al. Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres. Nature 526, 682–686 (2015).

    Article  CAS  PubMed  ADS  Google Scholar 

  43. Rosenfeld, W. et al. Event-ready Bell test using entangled atoms simultaneously closing detection and locality loopholes. Phys. Rev. Lett. 119, 010402 (2017).

    Article  PubMed  ADS  Google Scholar 

  44. Portmann, C. & Renner, R. Security in quantum cryptography. Preprint at https://arXiv.org/abs/2102.00021 (2021).

  45. Barrett, J., Colbeck, R. & Kent, A. Memory attacks on device-independent quantum cryptography. Phys. Rev. Lett. 110, 010503 (2013).

    Article  PubMed  ADS  Google Scholar 

  46. Pironio, S. et al. Random numbers certified by Bell’s theorem. Nature 464, 1021–1024 (2010).

    Article  CAS  PubMed  ADS  Google Scholar 

  47. Pironio, S. et al. Device-independent quantum key distribution secure against collective attacks. New J. Phys. 11, 045021 (2009).

    Article  ADS  Google Scholar 

  48. Pirandola, S. et al. Advances in quantum cryptography. Adv. Opt. Photon. 12, 1012–1236 (2020).

    Article  Google Scholar 

  49. Heshami, K. et al. Quantum memories: emerging applications and recent advances. J. Mod. Opt. 63, 2005–2028 (2016).

    Article  PubMed  PubMed Central  ADS  Google Scholar 

  50. Wright, T. A. et al. Two-way photonic interface for linking the Sr+ transition at 422 nm to the telecommunication C band. Phys. Rev. Appl. 10, 044012 (2018).

    Article  CAS  ADS  Google Scholar 

  51. Schupp, J. et al. Interface between trapped-ion qubits and traveling photons with close-to-optimal efficiency. PRX Quantum 2, 020331 (2021).

    Article  ADS  Google Scholar 

  52. Sangouard, N., Simon, C., de Riedmatten, H. & Gisin, N. Quantum repeaters based on atomic ensembles and linear optics. Rev. Mod. Phys. 83, 33–80 (2011).

    Article  ADS  Google Scholar 

  53. Bourdeauducq, S. et al. m-labs/artiq: 6.0. Zenodo https://doi.org/10.5281/zenodo.6619071 (2021).

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Acknowledgements

J.-D.B. and E.Y.-Z.T. thank R. Arnon-Friedman for discussions. We thank Sandia National Laboratories for supplying HOA2 ion traps. This work was supported by the UK Engineering and Physical Sciences Research Council Hub in Quantum Computing and Simulation (EP/T001062/1), the EU Quantum Technology Flagship Project AQTION (No. 820495) and the UKRI Fellowship of C.J.B. (MR/S03238X/1). E.Y.-Z.T. and R.R. acknowledge funding by the Swiss National Science Foundation, through the National Centers for Competence in Research QSIT and SwissMAP, and by the Air Force Office of Scientific Research through grant FA9550-19-1-0202. J.-D.B and N.S. acknowledge funding by the Institut de Physique Théorique, Commissariat á l’Énergie Atomique et aux Energies Alternatives and the Region Île-de-France in the framework of DIM SIRTEQ.

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Authors and Affiliations

  1. Clarendon Laboratory, Department of Physics, University of Oxford, Oxford, UK

    D. P. Nadlinger, P. Drmota, B. C. Nichol, G. Araneda, D. Main, R. Srinivas, D. M. Lucas & C. J. Ballance

  2. School of Computer and Communication Sciences, EPFL, Lausanne, Switzerland

    K. Ivanov & R. L. Urbanke

  3. Institute for Theoretical Physics, ETH Zürich, Zürich, Switzerland

    E. Y.-Z. Tan & R. Renner

  4. Department of Applied Physics, University of Geneva, Geneva, Switzerland

    P. Sekatski

  5. Université Paris-Saclay, CEA, CNRS, Institut de Physique Théorique, Gif-sur-Yvette, France

    N. Sangouard & J.-D. Bancal

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Contributions

D.P.N., P.D., B.C.N., G.A., D.M. and R.S. built and operated the experimental apparatus. D.P.N. and P.D. led the collection of the experimental data and performed the data analysis. J.-D.B. and D.P.N. extracted the key from the raw data. K.I., R.L.U. and J.-D.B. designed the error correction code. J.-D.B., E.Y.-Z.T., N.S., P.S. and R.R. established the detailed protocol steps and derived the corresponding security proof. N.S., J.-D.B., D.P.N. and C.J.B. wrote the manuscript. C.J.B. and D.M.L. supervised the experimental work, and J.-D.B. and N.S. supervised the theoretical work. N.S. and J.-D.B. initiated the project. All authors contributed to the discussion and interpretation of results, and contributed to the manuscript.

Corresponding authors

Correspondence to D. P. Nadlinger, C. J. Ballance, N. Sangouard or J.-D. Bancal.

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Competing interests

C.J.B. is a director of Oxford Ionics. The remaining authors declare no competing interests.

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Nature thanks Marcos Curty, Lynden Shalm and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

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Nadlinger, D.P., Drmota, P., Nichol, B.C. et al. Experimental quantum key distribution certified by Bell's theorem. Nature 607, 682–686 (2022). https://doi.org/10.1038/s41586-022-04941-5

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