Skip to main content
SpringerLink
Log in

Improved statistical fluctuation analysis for measurement-device-independent quantum key distribution

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

Measurement-device-independent quantum key distribution (MDI-QKD) is a promising protocol for realizing long-distance secret keys sharing. However, its key rate is relatively low when the finite-size effect is taken into account. In this paper, we consider statistical fluctuation analysis for the three-intensity decoy-state MDI-QKD system based on the recent work (Zhang et al. in Phys Rev A 95:012333, 2017) and further compare its performance with that of applying the Gaussian approximation technique and the Chernoff bound method. The numerical simulations demonstrate that the new method has apparent enhancement both in key generation rate and transmission distance than using Chernoff bound method. Meanwhile, the present work still shows much higher security than Gaussian approximation analysis.

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

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, 7–11 (2014)

    Article  MathSciNet  Google Scholar 

  2. Ekert, A.K.: Quantum cryptography based on Bells theorem. Phys. Rev. Lett. 67, 661–663 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  3. Lo, H.K., Chau, H.F.: Unconditional security of quantum key distribution over arbitrarily long distances. Science 283, 2050–2056 (1999)

    Article  ADS  Google Scholar 

  4. Shor, P.W., Preskill, J.: Simple proof of security of the BB84 quantum key distribution protocol. Phys. Rev. Lett. 85, 441–444 (2000)

    Article  ADS  Google Scholar 

  5. Mayers, D.: Unconditional security in quantum cryptography. J. ACM 48, 351–406 (2001)

    Article  MathSciNet  Google Scholar 

  6. Gottesman, D., Lo, H.K., Lutkenhaus, N., Preskill, J.: Security of quantum key distribution with imperfect devices. Quantum Inf. Comput. 4, 325–360 (2004)

    MathSciNet  MATH  Google Scholar 

  7. Brassard, G., Lutkenhaus, N., Mor, T., et al.: Limitations on practical quantum cryptography. Phys. Rev. Lett. 85, 1330–1333 (2000)

    Article  ADS  Google Scholar 

  8. Lutkenhaus, N.: Security against individual attacks for realistic quantum key distribution. Phys. Rev. A 5, 052304 (2000)

    Article  ADS  Google Scholar 

  9. Fung, C.H.F., Qi, B., Tamaki, K., Lo, H.K.: Phase-remapping attack in practical quantum-key-distribution systems. Phys. Rev. A 75, 032314 (2007)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  11. Qi, B., Fung, C.H.F., Lo, H.K., et al.: Time-shift attack in practical quantum cryptosystems. Quantum Inf. Comput. 7, 73–82 (2007)

    MathSciNet  MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

  13. Makarov, V., Hjelme, D.R.: Faked states attack on quantum cryptosystems. J. Mod. Opt. 52, 691–705 (2005)

    Article  ADS  Google Scholar 

  14. Makarov, V., Anisimov, A., Skaar, J.: Effects of detector efficiency mismatch on security of quantum cryptosystems. Phys. Rev. A 74, 022313 (2006)

    Article  ADS  Google Scholar 

  15. Hwang, W.Y.: Quantum key distribution with high loss: toward global secure communication. Phys. Rev. Lett. 91, 057901 (2003)

    Article  ADS  Google Scholar 

  16. Wang, X.B.: Beating the photon-number-splitting attack in practical quantum cryptography. Phys. Rev. Lett. 94, 230503 (2005)

    Article  ADS  Google Scholar 

  17. Lo, H.K., Ma, X.F., Chen, K.: Decoy state quantum key distribution. Phys. Rev. Lett. 94, 230504 (2005)

    Article  ADS  Google Scholar 

  18. Acin, A., Massar, S., Pironio, S.: Efficient quantum key distribution secure against no-signalling eavesdroppers. New J. Phys. 8, 126 (2006)

    Article  ADS  Google Scholar 

  19. Acin, A., Brunner, N., Gisin, N., et al.: Device-independent security of quantum cryptography against collective attacks. Phys. Rev. Lett. 98, 230501 (2007)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  21. Wang, X.B.: Three-intensity decoy-state method for device-independent quantum key distribution with basis-dependent errors. Phys. Rev. A 87, 012320 (2013)

    Article  ADS  Google Scholar 

  22. Wang, Q., Wang, X.B.: Efficient implementation of the decoy-state measurement-device-independent quantum key distribution with heralded single-photon sources. Phys. Rev. A 88, 052332 (2013)

    Article  ADS  Google Scholar 

  23. Tamaki, K., Lo, H.K., Fung, C.H.F., et al.: Phase encoding schemes for measurement-device-independent quantum key distribution with basis-dependent flaw. Phys. Rev. A 85, 42307 (2012)

    Article  ADS  Google Scholar 

  24. Ferreira da Silva, T., Vitoreti, D., Xavier, G.B., 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 

  25. Chen, D., Zhao, S.H., Shi, L., Liu, Y.: Measurement-device-independent quantum key distribution with pairs of vector vortex beams. Phys. Rev. A 93, 032320 (2015)

    Article  ADS  Google Scholar 

  26. Liu, Y., Chen, T.Y., Wang, L.J.: Experimental measurement-device-independent quantum key distribution. Phys. Rev. Lett. 111, 130502 (2013)

    Article  ADS  Google Scholar 

  27. Wang, C., Song, X.T., Yin, Z.Q.: Phase-reference-free experiment of measurement-device-independent quantum key distribution. Phys. Rev. Lett. 115, 160502 (2015)

    Article  ADS  Google Scholar 

  28. Yin, H.L., Chen, T.Y., Yu, Z.W.: Measurement-device-independent quantum key distribution over a 404 km optical fiber. Phys. Rev. Lett. 117, 190501 (2016)

    Article  ADS  Google Scholar 

  29. Wang, C., Yin, Z.Q., Wang, S., et al.: Measurement-device-independent quantum key distribution robust against environmental disturbances. Optica 4, 1016 (2017)

    Article  Google Scholar 

  30. Zhou, Y.H., Yu, Z.W., Wang, X.B.: Making the decoy-state measurement-device-independent quantum key distribution practically useful. Phys. Rev. A 93, 042324 (2016)

    Article  ADS  Google Scholar 

  31. Wei, J.H., Dai, H.Y., Zhang, M.: Two efficient schemes for probabilistic remote state preparation and the combination of both schemes. Quantum Inf. Process. 13, 2115–2125 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  32. Wei, J.H., Shi, L., et al.: Remote preparation of an arbitrary multi-qubit state via two-qubit entangled states. Quantum Inf. Process. 16, 2601–2612 (2016)

    MathSciNet  Google Scholar 

  33. Lim, C.C.W., Curty, M., Walenta, N., Xu, F.H., Zbinden, H.: Concise security bounds for practical decoy-state quantum key distribution. Phys. Rev. A 89, 022307 (2014)

    Article  ADS  Google Scholar 

  34. Curty, M., Xu, F.H., Cui, W., et al.: Finite-key analysis for measurement-device-independent quantum key distribution. Nat. Commun. 5, 3732 (2014)

    Article  Google Scholar 

  35. Yu, Z.W., Zhou, Y.H., Wang, X.B.: Statistical fluctuation analysis for measurement-device-independent quantum key distribution with three-intensity decoy-state method. Phys. Rev. A 91, 032318 (2015)

    Article  ADS  Google Scholar 

  36. Zhang, Z., Zhao, Q., Razavi, M., et al.: Improved key-rate bounds for practical decoy-state quantum-key-distribution systems. Phys. Rev. A 95, 012333 (2017)

    Article  ADS  Google Scholar 

  37. Ma, X.F., Fung, C.H.F., Razavi, M.: Statistical fluctuation analysis for measurement-device-independent quantum key distribution. Phys. Rev. A 86, 052305 (2012)

    Article  ADS  Google Scholar 

  38. Chernoff, H.: A measure of asymptotic efficiency for tests of a hypothesis based on the sum of observations. Ann. Math. Stat. 23, 493 (1952)

    Article  MathSciNet  Google Scholar 

  39. Jiang, C., Yu, Z.W., Wang, X.B.: Measurement-device-independent quantum key distribution with source state errors and statistical fluctuation. Phys. Rev. A 95, 032325 (2017)

    Article  ADS  Google Scholar 

  40. Wang, Q., Wang, X.B.: Simulating of the measurement-device independent quantum key distribution with phase randomized general sources. Sci. Rep. 4, 4612 (2014)

    Article  ADS  Google Scholar 

  41. Xu, F.H., Xu, H., Lo, H.K.: Protocol choice and parameter optimization in decoy-state measurement-device-independent quantum key distribution. Phys. Rev. A 89, 052333 (2014)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We appreciate enlightened discussion and kind assistance in mathematical simulations from Mr. X. Y. Zhou and C. H. Zhang. We also gratefully acknowledge the financial support from the National Key Research and Development Program of China through Grant No. 2017YFA0304100, the National Natural Science Foundation of China through Grants Nos. 61475197, 61590932, 11774180, 61705110, the Natural Science Foundation of the Jiangsu Higher Education Institutions through Grant Nos. 15KJA120002, 17KJB140016, the Outstanding Youth Project of Jiangsu Province through Grant No. BK20150039 and the Natural Science Foundation of Jiangsu Province through Grant No. BK20170902.

Author information

Authors and Affiliations

  1. Institute of Quantum Information and Technology, Nanjing University of Posts and Telecommunications, Nanjing, 210003, China

    Hua-Jian Ding, Chen-Chen Mao, Chun-Mei Zhang & Qin Wang

  2. Key Lab of Broadband Wireless Communication and Sensor Network Technology, Nanjing University of Posts and Telecommunications, Ministry of Education, Nanjing, 210003, China

    Hua-Jian Ding, Chen-Chen Mao, Chun-Mei Zhang & Qin Wang

Authors
  1. Hua-Jian Ding
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chen-Chen Mao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Chun-Mei Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Qin Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Qin Wang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ding, HJ., Mao, CC., Zhang, CM. et al. Improved statistical fluctuation analysis for measurement-device-independent quantum key distribution. Quantum Inf Process 17, 332 (2018). https://doi.org/10.1007/s11128-018-2026-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-018-2026-3

Keywords

Search

Navigation