Skip to main content

Advertisement

Log in

Fault-tolerant blind quantum computing using GHZ states over depolarization channel

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

Blind quantum computing (BQC) allows a client with limited quantum technology to delegate her quantum computational tasks to a server who can perform universal quantum computation while retaining the client’s secret information. Firstly, in qubits transmission between the server and the client, the loss of qubits is inevitable due to the channel noise. Thus, we propose a fault-tolerant framework for blind quantum computing using logical GHZ states over depolarization channels. In our protocol, an encoded GHZ state by 7-qubit Calderbank–Shor–Steane code is sent by the quantum channel as a medium of quantum teleportation. The client only makes a single-qubit measurement on the third qubit of the logical GHZ state, and the remaining Bell state is shared between the client and the server. After decoding logical Bell state, the client and the server perform the measurement-based blind quantum computing protocol. Secondly, there are two classes of collective noises in the channel, which will affect the blind quantum computing. We modify our BQC protocol to overcome the collective-dephasing noise and the collective-rotating noise with logical states \(|H_{dp}\rangle \), \(|V_{dp}\rangle \), \(|H_{r}\rangle \) and \(|V_{r}\rangle \). Our protocol is robust against channel noise and qubits loss.

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

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Fig. 1
Fig. 2

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

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, Bangalore, vol. 10–12, pp. 175–179 (1984)

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

    Article  ADS  Google Scholar 

  3. Bennett, C.H., Brassard, G., Crépeau, C., Jozsa, R., Peres, A., Wootters, W.K.: Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels. Phys. Rev. Lett. 70, 1895–1899 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  4. Andrew, M.: Childs, secure assisted quantum computation. Quant. Inform. Comput. 5, 456–466 (2005)

    Google Scholar 

  5. Fisher, K.A.G., Broadbent, A., Shalm, L.K., Yan, Z., Lavoie, J., Prevedel, R., Jennewein, T., Resch, K.J.: Quantum computing on encrypted data. Nat. Commun. 5, 3074 (2014)

    Article  ADS  Google Scholar 

  6. Fitzsimons, J.F.: Private quantum computation, an introduction to blind quantum computing and related protocols. NPJ Quant. Inform. 3, 23 (2017)

    Article  ADS  Google Scholar 

  7. Pablo, A., Louis, S.: Blind quantum computation. Int. J. Quant. Inform. 4, 883–898 (2006)

    Article  Google Scholar 

  8. Broadbent, A., Fitzsimons, J., Kashefi, E.: Universal blind quantum computation. In: 2009 50th Annual IEEE Symposium on Foundations of Computer Science, vol. 5, pp. 17–526 (2009)

  9. Briegel, H., Browne, D., Dür, W., Raussendorf, R., Van den Nest, M.: Measurement-based quantum computation. Nat. Phys. 5, 19–26 (2009)

    Article  Google Scholar 

  10. Broadbent, A., Fitzsimons, J., Kashefi, E.: Measurement-Based and Universal Blind Quantum Computation, vol. 4, pp. 3–86. Springer, Berlin (2010)

    MATH  Google Scholar 

  11. Barz, S., Kashefi, E., Broadbent, A., Fitzsimons, J.F., Zeilinger, A., Walther, P.: Demonstration of blind quantum computing. Science 335, 303–308 (2012)

    Article  ADS  MathSciNet  Google Scholar 

  12. Morimae, T., Fujii, K.: Secure entanglement distillation for double-server blind quantum computation. Phys. Rev. Lett. 111, 020502 (2013)

    Article  ADS  Google Scholar 

  13. Li, Q., Chan, W.H., Wu, C.H., Wen, Z.H.: Triple-server blind quantum computation using entanglement swapping. Phys. Rev. A 89, 040302 (2014)

    Article  ADS  Google Scholar 

  14. Tomoyuki, M., Keisuke, F.: Blind topological measurement-based quantum computation. Nat. Commun. 3, 1036 (2012)

    Article  Google Scholar 

  15. Raussendorf, R., Harrington, J.: Fault-tolerant quantum computation with high threshold in two dimensions. Phys. Rev. Lett. 99, 190504 (2007)

    Article  Google Scholar 

  16. Morimae, T., Fujii, K.: Blind quantum computation protocol in which Alice only makes measurements. Phys. Rev. A 87, 050301 (2013)

    Article  ADS  Google Scholar 

  17. Greganti, C., Roehsner, M.C., Barz, S., Morimae, T., Walther, P.: Demonstration of measurement-only blind quantum computing. N. J. Phys. 18, 013020 (2016)

    Article  Google Scholar 

  18. Takeuchi, Y., Fujii, K., Ikuta, R., Yamamoto, T., Imoto, N.: Blind quantum computation over a collective-noise channel. Phys. Rev. A 93, 052307 (2016)

    Article  ADS  Google Scholar 

  19. Bennett, C.H., Brassard, G., Popescu, S., Schumacher, B., Smolin, J.A., Wootters, W.K.: Purification of noisy entanglement and faithful teleportation via noisy channels. Phys. Rev. Lett. 76, 722–725 (1996)

    Article  ADS  Google Scholar 

  20. Dr, W., Briegel, H.J.: Entanglement purification and quantum error correction. Rep. Progress Phys. 70, 1381–1424 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  21. Zanardi, P., Rasetti, M.: Noiseless quantum codes. Phys. Rev. Lett. 79, 3306–3309 (1997)

    Article  ADS  Google Scholar 

  22. Sheng, Y.B., Zhou, L.: Deterministic entanglement distillation for secure double-server blind quantum computation. Cien. Rep. 5, 7815 (2015)

    Google Scholar 

  23. Kwiat, P.G., Berglund, A.J., Altepeter, J.B., White, A.G.: Experimental verification of decoherence-free subspaces. Science 260, 498–501 (2000)

    Article  ADS  Google Scholar 

  24. Tian-Yu, Y.: Fault-tolerant quantum dialogue without information leakage based on entanglement swapping between two logical bell states. Commun. Theor. Phys. 63, 431–438 (2015)

    Article  ADS  Google Scholar 

  25. Kumagai, H., Yamamoto, T., Koashi, M., Imoto, N.: Robustness of quantum communication based on a decoherence-free subspace using a counter-propagating weak coherent light pulse. Phys. Rev. A 87, 052325 (2013)

    Article  ADS  Google Scholar 

  26. Wu, D., Lv, H.J., Xie, G.J.: Robust anti-collective noise quantum secure direct dialogue using logical bell states. Int. J. Theor. Phys. 55, 1–13 (2015)

    MATH  Google Scholar 

  27. Stucki, D., Gisin, N., Guinnard, O., Ribordy, G., Zbinden, H.: Quantum key distribution over 67 km with a plugplay system. N. J. Phys. 4, 41 (2002)

    Article  Google Scholar 

  28. Yamamoto, T., Shimamura, J., Özdemir, Ş.K., Koashi, M., Imoto, N.: Faithful qubit distribution assisted by one additional qubit against collective noise. Phys. Rev. Lett. 95, 040503 (2005)

    Article  ADS  Google Scholar 

  29. Popescu, S., Rohrlich, D.: Quantum nonlocality as an axiom. Found. Phys. 24, 379–385 (1994)

    Article  ADS  MathSciNet  Google Scholar 

  30. Yang, C.W., Tsai, C.W., Hwang, T.: Fault tolerant deterministic quantum communications using GHZ states over collective-noise channels. Quant. Inform. Process. 12, 3043–3055 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  31. Zhang, X.Q., Weng, J., Lu, W., Li, X.C., Luo, W.Q., Tan, X.Q.: Greenberger–Horne–Zeilinger states-based blind quantum computation with entanglement concentration. Sci. Rep. 7, 11104 (2017)

    Article  ADS  Google Scholar 

  32. Ye, T.: Fault tolerant channel-encrypting quantum dialogue against collective noise. Sci. China Phys. Mech. Astron. 58, 1–10 (2015)

    Google Scholar 

  33. Gu, B., Mu, L., Ding, L.G., Zhang, C.Y., Li, C.Q.: Fault tolerant three-party quantum secret sharing against collective noise. Opt. Commun. 283, 3099–3103 (2010)

    Article  ADS  Google Scholar 

  34. Gu, B., Pei, S.X., Song, B., Zhong, K.: Deterministic secure quantum communication over a collective-noise channel. Sci. China Ser. G Phys. Mech. Astron. 52, 1913–1917 (2009)

    Article  ADS  Google Scholar 

  35. Xiao, M., Liu, L., Song, X.I.: Multi-server blind quantum computation over collective-noise channels. Quant. Inform. Process. 17, 63 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  36. Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information, 10th edn. Cambridge University Press, Cambridge (2011)

    MATH  Google Scholar 

Download references

Acknowledgements

The research is partly supported by the Natural Science Foundation of Guangdong Province of China under Grant No. 2019A1515011069, the National Cryptography Development Fund of China under Grant No. MMJJ20180109, the Major Program of Guangdong Basic and Applied Research under Grant No. 2019B030302008 and the National Natural Science Foundation of China under Grant Nos. 62032009 and 62005321.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Hong Tao.

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

Tan, X., Tao, H., Zhang, X. et al. Fault-tolerant blind quantum computing using GHZ states over depolarization channel. Quantum Inf Process 20, 297 (2021). https://doi.org/10.1007/s11128-021-03197-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-021-03197-8

Keywords

Navigation