Skip to main content
Log in

Afterpulse analysis for reference-frame-independent quantum key distribution

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

Reference-frame-independent quantum key distribution (RFI-QKD) can generate secret keys without the alignment of reference frames. However, in most RFI-QKD systems, the afterpulse inherent in single-photon avalanche detectors at the receiver’s side is always ignored, which will lead to a large deviation from the data obtained by the existing analytical models. In this paper, we establish an afterpulse-compatible analytical model to fix this deviation. Simulation results show that the secret key rate is overestimated when the afterpulse is ignored. Furthermore, based on the afterpulse-compatible model, we investigate the effect of the intensity fluctuation of the source at the transmitter’s side. Simulation results show that both the afterpulse and the intensity fluctuation affect the secret key rate, which should be carefully considered in practical RFI-QKD systems.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

References

  1. Bennett, C.H., Brassard, G.: Quantum Cryptography: Public Key Distribution and Coin Tossing. In: Proceedings of the IEEE international conference on computers, systems and signal processing, pp. 175–179 (1984)

  2. Long, G.-L., Liu, X.-S.: Theoretically efficient high-capacity quantum-key-distribution scheme. Phys. Rev. A 65(3), 032302 (2002). https://doi.org/10.1103/PhysRevA.65.032302

    Article  ADS  Google Scholar 

  3. Wu, X.-D., Zhou, L., Zhong, W., Sheng, Y.-B.: High-capacity measurement-device-independent quantum secure direct communication. Quantum Inf. Process. 19(10), 354 (2020). https://doi.org/10.1007/s11128-020-02864-6

    Article  ADS  MathSciNet  Google Scholar 

  4. Zhang, W., Ding, D.-S., Sheng, Y.-B., Zhou, L., Shi, B.-S., Guo, G.-C.: Quantum secure direct communication with quantum memory. Phys. Rev. Lett. 118(22), 220501 (2017). https://doi.org/10.1103/PhysRevLett.118.220501

    Article  ADS  Google Scholar 

  5. Sheng, Y.-B., Zhou, L., Long, G.-L.: One-step quantum secure direct communication. Sci. Bull. 67(4), 367–374 (2022). https://doi.org/10.1016/j.scib.2021.11.002

    Article  Google Scholar 

  6. Hillery, M., Bužek, V., Berthiaume, A.: Quantum secret sharing. Phys. Rev. A 59(3), 1829 (1999). https://doi.org/10.1103/PhysRevA.59.1829

    Article  ADS  MathSciNet  MATH  Google Scholar 

  7. Gu, J., Cao, X.-Y., Yin, H.-L., Chen, Z.-B.: Differential phase shift quantum secret sharing using a twin field. Opt. Express 29(6), 9165–9173 (2021). https://doi.org/10.1364/OE.417856

    Article  ADS  Google Scholar 

  8. Liao, Q., Liu, H., Zhu, L., Guo, Y.: Quantum secret sharing using discretely modulated coherent states. Phys. Rev. A 103(3), 032410 (2021). https://doi.org/10.1103/PhysRevA.103.032410

    Article  ADS  MathSciNet  Google Scholar 

  9. Giovannetti, V., Lloyd, S., Maccone, L.: Quantum private queries. Phys. Rev. Lett. 100(23), 230502 (2008). https://doi.org/10.1103/PhysRevLett.100.230502

    Article  ADS  MathSciNet  MATH  Google Scholar 

  10. Liu, B., Xia, S., Xiao, D., Huang, W., Xu, B., Li, Y.: Decoy-state method for quantum-key-distribution-based quantum private query. Sci. China Phys. Mech. 65(4), 240312 (2022). https://doi.org/10.1007/s11433-021-1843-7

    Article  Google Scholar 

  11. Ma, D., Liu, X., Huang, C., Chen, H., Lin, H., Wei, K.: Simple quantum key distribution using a stable transmitter-receiver scheme. Opt. Lett. 46(9), 2152–2155 (2021). https://doi.org/10.1364/OL.418851

    Article  ADS  Google Scholar 

  12. Wei, K., Li, W., Tan, H., Li, Y., Min, H., Zhang, W.-J., Li, H., You, L., Wang, Z., Jiang, X., et al.: High-speed measurement-device-independent quantum key distribution with integrated silicon photonics. Phys. Rev. X 10(3), 031030 (2020). https://doi.org/10.1103/PhysRevX.10.031030

    Article  Google Scholar 

  13. Zhang, Y., Chen, Z., Pirandola, S., Wang, X., Zhou, C., Chu, B., Zhao, Y., Xu, B., Yu, S., Guo, H.: Long-distance continuous-variable quantum key distribution over 202.81 km of fiber. Phys. Rev. Lett. 125(1), 010502 (2020). https://doi.org/10.1103/PhysRevLett.125.010502

    Article  ADS  Google Scholar 

  14. Tang, G.-Z., Li, C.-Y., Wang, M.: Polarization discriminated time-bin phase-encoding measurement-device-independent quantum key distribution. Quantum Eng. 3(4), 79 (2021). https://doi.org/10.1002/que2.79

    Article  Google Scholar 

  15. Wang, L., Zhao, S.: Round-robin differential-phase-shift quantum key distribution with heralded pair-coherent sources. Quantum Inf. Process. 16(4), 100 (2017). https://doi.org/10.1007/s11128-017-1550-x

    Article  ADS  MATH  Google Scholar 

  16. Peng, Q., Guo, Y., Liao, Q., Ruan, X.: Satellite-to-submarine quantum communication based on measurement-device-independent continuous-variable quantum key distribution. Quantum Inf. Process. 21(2), 61 (2022). https://doi.org/10.1007/s11128-022-03413-z

    Article  ADS  Google Scholar 

  17. Laing, A., Scarani, V., Rarity, J.G., O’Brien, J.L.: Reference-frame-independent quantum key distribution. Phys. Rev. A 82, 012304 (2010). https://doi.org/10.1103/PhysRevA.82.012304

    Article  ADS  Google Scholar 

  18. Yin, Z.-Q., Wang, S., Chen, W., Li, H.-W., Guo, G.-C., Han, Z.-F.: Reference-free-independent quantum key distribution immune to detector side channel attacks. Quantum Inf. Process. 13(5), 1237–1244 (2014). https://doi.org/10.1007/s11128-013-0726-2

    Article  ADS  MathSciNet  Google Scholar 

  19. Wang, C., Song, X.-T., Yin, Z.-Q., Wang, S., Chen, W., Zhang, C.-M., Guo, G.-C., Han, Z.-F.: Phase-reference-free experiment of measurement-device-independent quantum key distribution. Phys. Rev. Lett. 115(16), 160502 (2015). https://doi.org/10.1103/PhysRevLett.115.160502

    Article  ADS  Google Scholar 

  20. Zhang, C.-M., Zhu, J.-R., Wang, Q.: Practical decoy-state reference-frame-independent measurement-device-independent quantum key distribution. Phys. Rev. A 95(3), 032309 (2017). https://doi.org/10.1103/PhysRevA.95.032309

    Article  ADS  Google Scholar 

  21. Pramanik, T., Park, B.K., Cho, Y.-W., Han, S.-W., Kim, Y.-S., Moon, S.: Robustness of reference-frame-independent quantum key distribution against the relative motion of the reference frames. Phys. Lett. A 381(31), 2497–2501 (2017). https://doi.org/10.1016/j.physleta.2017.06.002

    Article  ADS  MathSciNet  MATH  Google Scholar 

  22. Zhou, X.-Y., Ding, H.-J., Sun, M.-S., Zhang, S.-H., Liu, J.-Y., Zhang, C.-H., Li, J., Wang, Q.: Reference-frame-independent measurement-device-independent quantum key distribution over 200 km of optical fiber. Phys. Rev. Appl. 15(6), 064016 (2021). https://doi.org/10.1103/PhysRevApplied.15.064016

    Article  ADS  Google Scholar 

  23. Chen, H., Wang, J., Tang, B., Li, Z., Liu, B., Sun, S.: Field demonstration of time-bin reference-frame-independent quantum key distribution via an intracity free-space link. Opt. Lett. 45(11), 3022–3025 (2020). https://doi.org/10.1364/OL.392742

    Article  ADS  Google Scholar 

  24. Zhu, J.-R., Wang, R., Zhang, C.-M.: Improved reference-frame-independent quantum key distribution. Opt. Lett. 47(16), 4219–4222 (2022). https://doi.org/10.1364/OL.470558

    Article  ADS  Google Scholar 

  25. Fan-Yuan, G.-J., Lu, F.-Y., Wang, S., Yin, Z.-Q., He, D.-Y., Chen, W., Zhou, Z., Wang, Z.-H., Teng, J., Guo, G.-C., et al.: Robust and adaptable quantum key distribution network without trusted nodes. Optica 9(7), 812–823 (2022). https://doi.org/10.1364/OPTICA.458937

    Article  ADS  Google Scholar 

  26. Lu, F.-Y., Yin, Z.-Q., Fan-Yuan, G.-J., Wang, R., Liu, H., Wang, S., Chen, W., He, D.-Y., Huang, W., Xu, B.-J., et al.: Efficient decoy states for the reference-frame-independent measurement-device-independent quantum key distribution. Phys. Rev. A 101(5), 052318 (2020). https://doi.org/10.1103/PhysRevA.101.052318

    Article  ADS  Google Scholar 

  27. Zhang, J., Itzler, M.A., Zbinden, H., Pan, J.-W.: Advances in ingaas/inp single-photon detector systems for quantum communication. Light: Sci. Appl. 4(5), 286–286 (2015). https://doi.org/10.1038/lsa.2015.59

    Article  Google Scholar 

  28. Fan-Yuan, G.-J., Wang, C., Wang, S., Yin, Z.-Q., Liu, H., Chen, W., He, D.-Y., Han, Z.-F., Guo, G.-C.: Afterpulse analysis for quantum key distribution. Phys. Rev. Appl. 10(6), 064032 (2018). https://doi.org/10.1103/PhysRevApplied.10.064032

    Article  ADS  Google Scholar 

  29. Wang, X.-B.: Beating the photon-number-splitting attack in practical quantum cryptography. Phys. Rev. Lett. 94, 230503 (2005). https://doi.org/10.1103/PhysRevLett.94.230503

    Article  ADS  Google Scholar 

  30. Lo, H.-K., Ma, X., Chen, K.: Decoy state quantum key distribution. Phys. Rev. Lett. 94, 230504 (2005). https://doi.org/10.1103/PhysRevLett.94.230504

    Article  ADS  Google Scholar 

  31. Wang, X.-B., Peng, C.-Z., Zhang, J., Yang, L., Pan, J.-W.: General theory of decoy-state quantum cryptography with source errors. Phys. Rev. A 77(4), 042311 (2008). https://doi.org/10.1103/PhysRevA.77.042311

    Article  ADS  Google Scholar 

  32. Wang, S., Zhang, S.-L., Li, H.-W., Yin, Z.-Q., Zhao, Y.-B., Chen, W., Han, Z.-F., Guo, G.-C.: Decoy-state theory for the heralded single-photon source with intensity fluctuations. Phys. Rev. A 79(6), 062309 (2009). https://doi.org/10.1103/PhysRevA.79.062309

    Article  ADS  Google Scholar 

  33. Ma, X., Qi, B., Zhao, Y., Lo, H.-K.: Practical decoy state for quantum key distribution. Phys. Rev. A 72, 012326 (2005). https://doi.org/10.1103/PhysRevA.72.012326

    Article  ADS  Google Scholar 

  34. Lim, C.C.W., Curty, M., Walenta, N., Xu, F., Zbinden, H.: Concise security bounds for practical decoy-state quantum key distribution. Phys. Rev. A 89(2), 022307 (2014). https://doi.org/10.1103/PhysRevA.89.022307

    Article  ADS  Google Scholar 

  35. Wang, F.-X., Chen, W., Li, Y.-P., He, D.-Y., Wang, C., Han, Y.-G., Wang, S., Yin, Z.-Q., Han, Z.-F.: Non-markovian property of afterpulsing effect in single-photon avalanche detector. J. Light. Technol. 34(15), 3610–3615 (2016). https://doi.org/10.1109/JLT.2016.2577141

    Article  ADS  Google Scholar 

  36. Hoeffding, W.: Probability inequalities for sums of bounded random variables. J. Amer. Stat. Assoc. 58(301), 13–30 (1963). https://doi.org/10.1080/01621459.1963.10500830

    Article  MathSciNet  MATH  Google Scholar 

  37. Zhu, J.-R., Li, J., Zhang, C.-M., Wang, Q.: Parameter optimization in biased decoy-state quantum key distribution with both source errors and statistical fluctuations. Quantum Inf. Process. 16(10), 238 (2017). https://doi.org/10.1007/s11128-017-1687-7

    Article  ADS  MathSciNet  MATH  Google Scholar 

  38. Wang, W.-J., Zhou, X.-Y., Zhang, C.-H., Ding, H.-J., Wang, Q.: Performance influence on reference-frame-independentquantum key distributions with detection imperfections. Quantum Inf. Process. 21(8), 283 (2022). https://doi.org/10.1007/s11128-022-03591-w

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This work was supported by China Postdoctoral Science Foundation (2019T120446, 2018M642281), Jiangsu Planned Projects for Postdoctoral Research Funds (2018K185C), the Natural Science Foundation of Nanjing University of Posts and Telecommunications (NY221058, 1311).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Chun-Mei Zhang.

Additional information

Publisher's Note

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

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nie, YF., Zhang, CM. Afterpulse analysis for reference-frame-independent quantum key distribution. Quantum Inf Process 21, 340 (2022). https://doi.org/10.1007/s11128-022-03688-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-022-03688-2

Keywords

Navigation