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Device-independent quantum random-number generation

Abstract

Randomness is important for many information processing applications, including numerical modelling and cryptography1,2. Device-independent quantum random-number generation (DIQRNG)3,4 based on the loophole-free violation of a Bell inequality produces genuine, unpredictable randomness without requiring any assumptions about the inner workings of the devices, and is therefore an ultimate goal in the field of quantum information science5,6,7. Previously reported experimental demonstrations of DIQRNG8,9 were not provably secure against the most general adversaries or did not close the ‘locality’ loophole of the Bell test. Here we present DIQRNG that is secure against quantum and classical adversaries10,11,12. We use state-of-the-art quantum optical technology to create, modulate and detect entangled photon pairs, achieving an efficiency of more than 78 per cent from creation to detection at a distance of about 200 metres that greatly exceeds the threshold for closing the ‘detection’ loophole of the Bell test. By independently and randomly choosing the base settings for measuring the entangled photon pairs and by ensuring space-like separation between the measurement events, we also satisfy the no-signalling condition and close the ‘locality’ loophole of the Bell test, thus enabling the realization of the loophole-free violation of a Bell inequality. This, along with a high-voltage, high-repetition-rate Pockels cell modulation set-up, allows us to accumulate sufficient data in the experimental time to extract genuine quantum randomness that is secure against the most general adversaries. By applying a large (137.90 gigabits × 62.469 megabits) Toeplitz-matrix hashing technique, we obtain 6.2469 × 107 quantum-certified random bits in 96 hours with a total failure probability (of producing a random number that is not guaranteed to be perfectly secure) of less than 10−5. Our demonstration is a crucial step towards transforming DIQRNG from a concept to a key aspect of practical applications that require high levels of security and thus genuine randomness7. Our work may also help to improve our understanding of the origin of randomness from a fundamental perspective.

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Fig. 1: Schematics of the experiment.
Fig. 2: Space–time diagram for the experimental design.
Fig. 3: Randomness generation versus number of trials.

Data availability

The data that support the findings of this study are available from the corresponding authors on reasonable request. Source Data for Fig. 3 is provided with the online version of the paper.

References

  1. Shannon, C. E. Communication theory of secrecy systems. Bell Labs Tech. J. 28, 656–715 (1949).

    Article  MathSciNet  Google Scholar 

  2. Metropolis, N. & Ulam, S. The Monte Carlo method. J. Am. Stat. Assoc. 44, 335–341 (1949).

    Article  CAS  Google Scholar 

  3. Colbeck, R. Quantum and Relativistic Protocols for Secure Multi-party Computation. PhD thesis, Cambridge Univ. (2009).

  4. Mayers, D. & Yao, A. Quantum cryptography with imperfect apparatus. In Proc. 39th Annual Symposium on Foundations of Computer Science (ed. Motwani, R.) 503–509 (IEEE, 1998).

  5. Ma, X., Yuan, X., Cao, Z., Qi, B. & Zhang, Z. Quantum random number generation. npj Quantum Inf. 2, 16021 (2016).

    Article  ADS  Google Scholar 

  6. Herrero-Collantes, M. & Garcia-Escartin, J. C. Quantum random number generators. Rev. Mod. Phys. 89, 015004 (2017).

    Article  ADS  MathSciNet  Google Scholar 

  7. Acín, A. & Masanes, L. Certified randomness in quantum physics. Nature 540, 213–219 (2016).

    Article  ADS  Google Scholar 

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

    Article  CAS  ADS  Google Scholar 

  9. Bierhorst, P. et al. Experimentally generated randomness certified by the impossibility of superluminal signals. Nature 556, 223–226 (2018).

    Article  CAS  ADS  Google Scholar 

  10. Miller, C. A. & Shi, Y. Universal security for randomness expansion from the spot-checking protocol. SIAM J. Comput. 46, 1304–1335 (2017).

    Article  MathSciNet  Google Scholar 

  11. Vazirani, U. V. & Vidick, T. Certifiable quantum dice - or, testable exponential randomness expansion. Preprint at https://arxiv.org/abs/1111.6054 (2011).

  12. Arnon-Friedman, R., Renner, R. & Vidick, T. Simple and tight device-independent security proofs. Preprint at https://arxiv.org/abs/1607.01797 (2016).

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

    Article  CAS  ADS  Google Scholar 

  14. Shalm, L. K. et al. Strong loophole-free test of local realism. Phys. Rev. Lett. 115, 250402 (2015).

    Article  ADS  Google Scholar 

  15. Giustina, M. et al. Significant-loophole-free test of Bell’s theorem with entangled photons. Phys. Rev. Lett. 115, 250401 (2015).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  18. Miller, C. A. & Shi, Y. Robust protocols for securely expanding randomness and distributing keys using untrusted quantum devices. J. ACM 63, 33 (2016).

    Article  MathSciNet  Google Scholar 

  19. Chung, K.-M., Shi, Y. & Wu, X. Physical randomness extractors: generating random numbers with minimal assumptions. Preprint at https://arxiv.org/abs/1402.4797 (2014).

  20. Coudron, M. & Yuen, H. Infinite randomness expansion with a constant number of devices. In Proc. 46th Annual ACM Symposium on Theory of Computing (ed. Shmoys, D.) 427–436 (ACM, 2014).

  21. Dupuis, F., Fawzi, O. & Renner, R. Entropy accumulation. Preprint at https://arxiv.org/abs/1607.01796 (2016).

  22. Liu, Y. et al. High-speed device-independent quantum random number generation without a detection loophole. Phys. Rev. Lett. 120, 010503 (2018).

    Article  CAS  ADS  Google Scholar 

  23. Clauser, J. F., Horne, M. A., Shimony, A. & Holt, R. A. Proposed experiment to test local hidden-variable theories. Phys. Rev. Lett. 23, 880–884 (1969).

    Article  ADS  Google Scholar 

  24. Coudron, M., Vidick, T. & Yuen, H. Robust randomness amplifiers: upper and lower bounds. In Proc. APPROX 2013: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (eds Raghavendra, P. et al.) 468–483 (Springer, 2013).

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

    Article  ADS  Google Scholar 

  26. Pereira, M. D. C. et al. Demonstrating highly symmetric single-mode, single-photon heralding efficiency in spontaneous parametric downconversion. Opt. Lett. 38, 1609–1611 (2013).

    Article  ADS  Google Scholar 

  27. Eberhard, P. H. Background level and counter efficiencies required for a loophole-free Einstein-Podolsky-Rosen experiment. Phys. Rev. A 47, R747–R750 (1993).

    Article  CAS  ADS  Google Scholar 

  28. Zhang, Y., Glancy, S. & Knill, E. Asymptotically optimal data analysis for rejecting local realism. Phys. Rev. A 84, 062118 (2011).

    Article  ADS  Google Scholar 

  29. Kessler, M. & Arnon-Friedman, R. Device-independent randomness amplification and privatization. Preprint at https://arxiv.org/abs/1705.04148 (2017).

  30. Bennink, R. Optimal collinear Gaussian beams for spontaneous parametric down-conversion. Phys. Rev. A 81, 053805 (2010).

    Article  ADS  Google Scholar 

  31. Dixon, P. B. et al. Heralding efficiency and correlated-mode coupling of near-IR fiber-coupled photon pairs. Phys. Rev. A 90, 043804 (2014).

    Article  ADS  Google Scholar 

  32. Zhang, W. et al. NbN superconducting nanowire single photon detector with efficiency over 90% at 1550 nm wavelength operational at compact cryocooler temperature. Sci. China Phys. Mechan. Astron. 60, 120314 (2017).

    Article  Google Scholar 

Download references

Acknowledgements

We thank S.-R. Zhao, Y.-H. Li, L.-K. Chen and R. Jin for experimental assistance, J. Zhong and S.-C. Shi for low-temperature system maintenance, and T. Peng, Y. Cao, C.-Z. Peng and Y.-A. Chen for discussions. This work was supported by the National Key R&D Program of China (2017YFA0303900, 2017YFA0304000), the National Natural Science Foundation of China, the Chinese Academy of Sciences and the Anhui Initiative in Quantum Information Technologies.

Reviewer information

Nature thanks R. Colbeck and the other anonymous reviewer(s) for their contribution to the peer review of this work.

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Authors and Affiliations

Authors

Contributions

X.M., J.F., Q.Z. and J.-W.P. conceived the research. Y.L., X.M., J. F., Q.Z. and J.-W.P. designed the experiment. Y.L., M.-H.L. and C.W. designed and implemented the source of entangled photon pairs. W.-Z.L. and J.-Y.G. designed the data acquisition software. W.Z., H.L., Z.W. and L.Y. fabricated and characterized the superconducting nanowire single-photon detector. B.B. and J.Z. designed the quantum random-number generators for the measurement setting choices. Q. Zhao, X.Y. and X.M. performed the protocol analysis, numerical modelling and randomness extraction. Y.Z. and W.J.M. performed the hypothesis tests. All authors contributed to the experimental realization, data analysis and manuscript preparation. J.-W.P. supervised the project.

Corresponding authors

Correspondence to Xiongfeng Ma, Jingyun Fan, Qiang Zhang or Jian-Wei Pan.

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The authors declare no competing interests.

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Supplementary information

Supplementary Information

This file contains Supplementary Text, Supplementary Figures 1-6, and Supplementary Tables 1-7. The Supplementary Information describes the theory of DIQRNG (Section I), the experimental details (Section II), and the experimental results (Section III).

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Liu, Y., Zhao, Q., Li, MH. et al. Device-independent quantum random-number generation. Nature 562, 548–551 (2018). https://doi.org/10.1038/s41586-018-0559-3

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