Skip to main content
SpringerLink
Log in

Practical source-independent quantum random number generation with detector efficiency mismatch

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

Quantum random number generators (QRNGs) are widely used in information processing tasks. The quality of the random numbers obtained from QRNGs relies on the accurate characterization of the physical implementations. In practice, realistic devices are difficult to characterize, resulting in incorrect entropy estimations of the output random numbers. Recently, a novel quantum random number generation (QRNG) scheme, referred to as source-independent QRNG (SIQRNG), has attracted a lot of interest. The scheme can provide certified randomness by using untrusted and uncharacterized sources, under the assumption that the measurement devices are trusted. However, realistic devices inevitably feature imperfections. Here, we show that the output randomness of SIQRNG is compromised in the presence of detection imperfection , by constructing an attack based on a time-domain detection efficiency mismatch between two practical detectors. More importantly, we provide an unconditional security proof of SIQRNG that takes detection efficiency mismatch into account. In addition, we provide a parameter optimization method to effectively improve the final random number generation rate. Our work demonstrates that SIQRNG is highly practical and that randomness can be extracted even in the presence of a detection efficiency mismatch.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  1. Bennett, C.H., Brassard, G.: Quantum cryptography: Public key distribution and coin tossing. Theor. Comput. Sci. 560, 7 (2014)

    MathSciNet  MATH  Google Scholar 

  2. Xu, F., Ma, X., Zhang, Q., Lo, H.-K., Pan, J.-W.: Secure quantum key distribution with realistic devices. Rev. Mod. Phys. 92, 025002 (2020)

    ADS  MathSciNet  Google Scholar 

  3. Wang, C., Deng, F.-G., Li, Y.-S., Liu, X.-S., Long, G.L.: Quantum secure direct communication with high-dimension quantum superdense coding. Phys. Rev. A 71, 044305 (2005)

    ADS  Google Scholar 

  4. Hu, J.-Y., Yu, B., Jing, M.-Y., Xiao, L.-T., Jia, S.-T., Qin, G.-Q., Long, G.-L.: Experimental quantum secure direct communication with single photons. Light Sci Appl. 5, e16144 (2016)

    Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  MathSciNet  Google Scholar 

  7. Dynes, J.F., Yuan, Z.L., Sharpe, A.W., Shields, A.J.: A high speed, postprocessing free, quantum random number generator. Appl. Phys. Lett. 93, 031109 (2008)

    ADS  Google Scholar 

  8. Wayne, M.A., Kwiat, P.G.: Low-bias high-speed quantum random number generator via shaped optical pulses. Opt. Express 18, 9351 (2010)

    ADS  Google Scholar 

  9. Gabriel, C., Wittmann, C., Sych, D., Dong, R., Mauerer, W., Andersen, U.L., Marquardt, C., Leuchs, G.: A generator for unique quantum random numbers based on vacuum states. Nat. Photon. 4, 711 (2010)

    ADS  Google Scholar 

  10. Shen, Y., Tian, L., Zou, H.: Practical quantum random number generator based on measuring the shot noise of vacuum states. Phys. Rev. A 81, 063814 (2010)

    ADS  Google Scholar 

  11. Symul, T., Assad, S.M., Lam, P.K.: Real time demonstration of high bitrate quantum random number generation with coherent laser light. Appl. Phys. Lett. 98, 231103 (2011)

    ADS  Google Scholar 

  12. Jofre, M., Curty, M., Steinlechner, F., Anzolin, G., Torres, J.P., Mitchell, M.W., Pruneri, V.: True random numbers from amplified quantum vacuum. Opt. Express 19, 20665 (2011)

    ADS  Google Scholar 

  13. Shi, Y., Chng, B., Kurtsiefer, C.: Random numbers from vacuum fluctuations. Appl. Phys. Lett. 109, 041101 (2016)

    ADS  Google Scholar 

  14. Zhou, Q., Valivarthi, R., John, C., et al.: Practical quantum random number generator based on sampling vacuum fluctuations. arXiv:1703.00559 (2017)

  15. Nie, Y.-Q., Zhang, H.-F., Zhang, Z., Wang, J., Ma, X., Zhang, J., Pan, J.-W.: Practical and fast quantum random number generation based on photon arrival time relative to external reference. Appl. Phys. Lett. 104, 110 (2014)

    ADS  Google Scholar 

  16. Qi, B., Chi, Y.-M., Lo, H.-K., Qian, L.: Practical and fast quantum random number generation based on photon arrival time relative to external reference. Opt. Lett. 35, 312 (2010)

    ADS  Google Scholar 

  17. Xu, F., Qi, B., Ma, X., Xu, H., Zheng, H., Lo, H.-K.: Ultrafast quantum random number generation based on quantum phase fluctuations. Opt. Express 20, 12366 (2012)

    ADS  Google Scholar 

  18. Nie, Y.-Q., Huang, L., Liu, Y., Payne, F., Zhang, J., Pan, J.-W.: The generation of 68 Gbps quantum random number by measuring laser phase fluctuations. Rev. Sci. Instrum. 86, 063105 (2015)

    ADS  Google Scholar 

  19. Abellán, C., Amaya, W., Mitrani, D., Pruneri, V., Mitchell, M.W.: Generation of Fresh and Pure Random Numbers for Loophole-Free Bell Tests. Phys. Rev. Lett. 115, 250403 (2015)

    ADS  Google Scholar 

  20. Zhang, X.-G., Nie, Y.-Q., Zhou, H., Liang, H., Ma, X., Zhang, J., Pan, J.-W.: Fully integrated 32 Gbps quantum random number generator with real-time extraction, Rev. Sci. Instrum. 87, 102 (2016)

    ADS  Google Scholar 

  21. Sun, S.-H., Xu, F.: Experimental study of a quantum random-number generator based on two independent lasers. Phys. Rev. A 96, 062314 (2017)

    ADS  Google Scholar 

  22. http://www.quantum-info.com; http://www.qutools.com; http://www.idquantique.com

  23. Wei, K., Ma, H., Yang, X.J.: Feasible attack on detector-device-independent quantum key distribution. Opt. Soc. Am. B 34, 2185 (2017)

    ADS  Google Scholar 

  24. Pironio, S., Acín, A., Massar, S., de la Giroday, A.B., Matsukevich, D.N., Maunz, P., Olmschenk, S., Hayes, D., Luo, L., Manning, T.A., Monroe, C.: Random numbers certified by Bell’s theorem. Nature 464, 1021 (2010)

    ADS  Google Scholar 

  25. Colbeck, R., Kent, A.: Private randomness expansion with untrusted devices. Journal of Physics A: Mathematical and Theoretical 44, 095305 (2011)

    ADS  MathSciNet  MATH  Google Scholar 

  26. Liu, Y., Yuan, X., Li, M.-H., Zhang, W., Zhao, Q., Zhong, J., Cao, Y., Li, Y.-H., Chen, L.-K., Li, H., Peng, T., Chen, Y.-A., Peng, C.-Z., Shi, S.-C., Wang, Z., You, L., Ma, X., Fan, J., Zhang, Q., Pan, J.-W.: High-Speed Device-Independent Quantum Random Number Generation without a Detection Loophole. Phys. Rev. Lett. 120, 010503 (2018)

    ADS  Google Scholar 

  27. Li, M.-H., Zhang, X., Liu, W.-Z., Zhao, S.-R., Bai, B., Liu, Y., Zhao, Q., Peng, Y., Zhang, J., Ma, X., Zhang, Q., Fan, J., Pan, J.-W.: Experimental realization of device-independent quantum randomness expansion. arXiv: 1902.07529 (2019)

  28. Bierhorst, P., Knill, E., Glancy, S., Zhang, Y., Mink, A., Jordan, S., Rommal, A., Liu, Y.-K., Christensen, B., Nam, S.W., Stevens, M.J., Shalm, L.K.: Experimentally generated randomness certified by the impossibility of superluminal signals. Nature 556, 223 (2018)

    ADS  Google Scholar 

  29. Liu, Y., Zhao, Q., Li, M.-H., Guan, J.-Y., Zhang, Y., Bai, B., Zhang, W., Liu, W.-Z., Wu, C., Yuan, X., Li, H., Munro, W.J., Wang, Z., You, L., Zhang, J., Ma, X., Fan, J., Zhang, Q., Pan, J.-W.: Device-independent quantum random-number generation. Nature 562, 548 (2018)

    ADS  Google Scholar 

  30. Li, H.-W., Yin, Z.-Q., Wu, Y.-C., Zou, X.-B., Wang, S., Chen, W., Guo, G.-C., Han, Z.-F.: Attacking a practical quantum-key-distribution system with wavelength-dependent beam-splitter and multiwavelength sources. Phys. Rev. A 84, 034301 (2011)

    ADS  Google Scholar 

  31. Bowles, J., Quintino, M.T., Brunner, N.: Certifying the dimension of classical and qquantum systems in a prepare-and-measure scenario with independent devices. Phys. Rev. Lett. 112, 140407 (2014)

    ADS  Google Scholar 

  32. Zhu, C., Hongyi, Z., Xiongfeng, M.: Loss-tolerant measurement-device-independent quantum random number generation. New J. Phys. 17, 125011 (2015)

    Google Scholar 

  33. Ma, J., Hakande, A., Yuan, X., Ma, X.: Coherence as a resource for source-independent quantum random-number generation, Phys. Rev. A 99, 022328 (2019)

    ADS  Google Scholar 

  34. Lunghi, T., Brask, J.B., Lim, C.C.W., Lavigne, Q., Bowles, J., Martin, A., Zbinden, H., Brunner, N.: Self-Testing Quantum Random Number Generator. Phys. Rev. Lett. 114, 150501 (2015)

    ADS  Google Scholar 

  35. Xu, F., Shapiro, J.H., Wong, F.N.C.: Experimental fast quantum random number generation using high-dimensional entanglement with entropy monitoring. Optica 3, 1266 (2016)

    ADS  Google Scholar 

  36. Nie, Y.-Q., Guan, J.-Y., Zhou, H., Zhang, Q., Ma, X., Zhang, J., Pan, J.-W.: Experimental measurement-device-independent quantum random-number generation. Phys. Rev. A 94, 060301 (2016)

    ADS  Google Scholar 

  37. Marangon, D.G., Vallone, G., Villoresi, P.: Source-Device-Independent Ultrafast Quantum Random Number Generation. Phys. Rev. Lett. 118, 060503 (2017)

    ADS  Google Scholar 

  38. Brask, J.B., Martin, A., Esposito, W., Houlmann, R., Bowles, Z.J., Zbinden, H., Brunner, N.: Megahertz-Rate Semi-Device-Independent Quantum Random Number Generators Based on Unambiguous State Discrimination. Phys. Rev. Applied 7, 054018 (2017)

    ADS  Google Scholar 

  39. Xu, B., Chen, Z., Li, Z., Yang, J., Su, Q., Huang, W., Zhang, Y., Guo, H.: High speed continuous variable source-independent quantum random number generation. Quantum. Sci. Technol. 4, 025013 (2019)

    ADS  Google Scholar 

  40. Smith, P.R., Marangon, D.G., Lucamarini, M., Yuan, Z.L., Shields, A.J.: Simple source device-independent continuous-variable quantum random number generator. Phys. Rev. A 99, 062326 (2019)

    ADS  Google Scholar 

  41. Cao, Z., Zhou, H., Yuan, X., Ma, X.: Source-Independent Quantum Random Number Generation. Phys. Rev. X 6, 011020 (2016)

    Google Scholar 

  42. Avesani, M., Marangon, D.G., Vallone, G., Villoresi, P.: Source-device-independent heterodyne-based quantum random number generator at 17 Gbps. Nat. Commum. 9, 5365 (2018)

    ADS  Google Scholar 

  43. Li, Y.-H., Han, X., Cao, Y., Yuan, X., Li, Z.-P., Guan, J.-Y., Yin, J., Zhang, Q., Ma, X., Peng, C.-Z., Pan, J.-W.: Quantum random number generation with uncharacterized laser and sunlight. Npj Quantum Inf. 5, 97 (2019)

    ADS  Google Scholar 

  44. Huang, A., Barz, S., Andersson, E., Makarov, V.: Implementation vulnerabilities in general quantum cryptography. New J. Phys. 20, 103016 (2018)

    ADS  Google Scholar 

  45. Li H-W, Wang S, Huang J-Z, Chen W, Yin Z-Q, Li F-Y, Zhou Z, Liu D, Zhang Y, Guo G-C, Bao W-S, Han Z-F: Attacking a practical quantum-key-distribution system with wavelength-dependent beam-splitter and multiwavelength sources. Phys. Rev. A 84, 062308 (2011)

    ADS  Google Scholar 

  46. Wei, K., Liu, H., Ma, H., Yang, X., Zhang, Y., Sun, Y., Xiao, J., Ji, Y.: Feasible attack on detector-device-independent quantum key distribution. Sci. Rep. 7, 449 (2017)

    ADS  Google Scholar 

  47. Makarov, V., Anisimov, A., Skaar, J.: Effects of detector efficiency mismatch on security of quantum cryptosystems. Phys. Rev. A 74, 002313 (2006)

    ADS  Google Scholar 

  48. Wei, K., Zhang, W., Tang, Y.-L., You, L., Xu, F.: Implementation security of quantum key distribution due to polarization-dependent efficiency mismatch. Phys. Rev. A 100, 022325 (2019)

    ADS  Google Scholar 

  49. Sajeed S, Chaiwongkhot P, Bourgoin JP, Jennewein T, Lutkenhaus N, Makarov V: Security loophole in free-space quantum key distribution due to spatial-mode detector-efficiency mismatch Shihan. Phys. Rev. 91, 301 (2015)

    ADS  Google Scholar 

  50. Qi, B., Fred, F.C.-H., Lo, H.-K., Ma, X.: Time-shift attack in practical quantum cryptosystems. Quant. Inf. Comput. 7, 73 (2007)

    MathSciNet  MATH  Google Scholar 

  51. Hensen, B., Bernien, H., Dréau, A.E., Reiserer, A., Kalb, N., Blok, M.S., Ruitenberg, J., Vermeulen, R.F.L., Schouten, R.N., Abellán, C., Amaya, W., Pruneri, V., Mitchell, M.W., Markham, M., Twitchen, D.J., Elkouss, D., Wehner, S., Taminiau, T.H., Hanson, R.: Loophole-free Bell inequality violation using electron spins separated by 13 kilometres. Nature 526, 682 (2015)

    ADS  Google Scholar 

  52. Fung, C.-H.F., Tamaki, K., Qi, B., Lo, H.-K., Ma, X.: Security proof of quantum key distribution with detection efficiency mismatch. Quantum Info. Comput. 9, 131 (2009)

    MathSciNet  MATH  Google Scholar 

  53. Ma, X., Xu, F., Xu, H., Tan, X., Qi, B., Lo, H.-K.: Postprocessing for quantum random-number generators: Entropy evaluation and randomness extraction. Phys. Rev. A 87, 062327 (2013)

    ADS  Google Scholar 

  54. Ma, X., Qi, B., Zhao, Y., Lo, H.-K.: Practical decoy state for quantum key distribution. Phys. Rev. A 72, 012326 (2005)

    ADS  Google Scholar 

  55. Xu, F., Qi, B., Lo, H.-K.: Experimental demonstration of phase-remapping attack in a practical quantum key distribution system. New J. Phys. 12, 113026 (2010)

    ADS  Google Scholar 

  56. Henning, W., Harald, K., Markus, R., Martin, F., Sebastian, N., Harald, W.: Quantum eavesdropping without interception: an attack exploiting the dead time of single-photon detectors. New J. Phys. 13, 073024 (2011)

    Google Scholar 

  57. Bouda, J., Pivoluska, M., Plesch, M., Wilmott, C.: Weak randomness seriously limits the security of quantum key distribution. Phys. Rev. A 86, 062308 (2012)

    ADS  Google Scholar 

  58. Lydersen, L., Wiechers, C., Wittmann, C., Elser, D., Skaar, J., Makarov, V.: Hacking commercial quantum cryptography systems by tailored bright illumination. Nature Photon. 4, 686 (2010)

    ADS  Google Scholar 

  59. Li, H.-W., Wang, S., Huang, J.-Z., Chen, W., Yin, Z.-Q., Li, F.-Y., Zhou, Z., Liu, D., Zhang, Y., Guo, G.-C., Bao, W.-S., Han, Z.-F.: Attacking a practical quantum-key-distribution system with wavelength-dependent beam-splitter and multiwavelength sources. Phys. Rev. A 84, 062308 (2011)

    ADS  Google Scholar 

Download references

Acknowledgements

We especially thank Dr. Yu-Huai Li for helpful discussions and Huihe Chen for English language revisions. This work was supported by the National Natural Science Foundation of China (No. 61705048 and No. 11865004) and the Guangxi Science Foundation (Grant No. 2017GXNSFBA198231).

Author information

Authors and Affiliations

  1. Guangxi Key Laboratory for Relativistic Astrophysics, School of Physics Science and Technology, Guangxi University, Nanning, 530004, China

    Di Ma, Yangpeng Wang & Kejin Wei

Authors
  1. Di Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yangpeng Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Kejin Wei
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Kejin Wei.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ma, D., Wang, Y. & Wei, K. Practical source-independent quantum random number generation with detector efficiency mismatch. Quantum Inf Process 19, 384 (2020). https://doi.org/10.1007/s11128-020-02865-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-020-02865-5

Search

Navigation