Analysis of weighted quantum secret sharing based on matrix product states | Quantum Information Processing Skip to main content
Springer Nature Link
Log in

Analysis of weighted quantum secret sharing based on matrix product states

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

In this paper, motivated by the usefulness of tensor networks to quantum information theory for the progress in study of entanglement in quantum many-body systems, we apply the hexagon tensor network algorithms in terms of Holland’s theory to study the weight allocation and dynamic problems in weighted quantum secret sharing that are not well solved by existing approaches with near-term devices and avoid the instability in the allocation of participants. To be exact, the variety of matrix product state representation of any quantum many-body state can be used to realize dynamic quantum state secret sharing.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
¥17,985 /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 includes VAT (Japan)

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

Similar content being viewed by others

Explore related subjects

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

References

  1. Vidal, G.: Emcient classical simulation of slightly entangled quantum computations. Phys. Rev. Lett. 91(14), 147902 (2003)

    Article  ADS  Google Scholar 

  2. Vidal, G.: Efficient simulation of one-dimensional quantum many-body systems. Phys. Rev. Lett. 93(4), 040502 (2004)

    Article  ADS  Google Scholar 

  3. Vidal, G.: Classical simulation of infinite-size quantum lattice systems in one spatial dimension. Phys. Rev. Lett. 98(7), 070201 (2007)

    Article  ADS  Google Scholar 

  4. Verstraete, F., Porras, D., Cirac, J.I.: Density matrix renormalization group and periodic boundary conditions: a quantum information perspective. Phys. Rev. Lett. 93(22), 227205 (2004)

    Article  ADS  Google Scholar 

  5. Schollwöck, U.: The density-matrix renormalization group in the age of matrix product states. Ann. Phys. 326(1), 96–192 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  6. Navascués, M., Singh, S., Acín, A.: Connector tensor networks: a renormalization-type approach to quantum certification. Phys. Rev. X 10(2), 021064 (2020)

    Google Scholar 

  7. Zhao, H.H., Xie, Z.Y., Chen, Q.N., Wei, Z.C., Cai, J.W., Xiang, T.: Renormalization of tensor-network states. Phys. Rev. B. 81(17), 174411 (2010)

    Article  ADS  Google Scholar 

  8. Levin, M., Nave, C.P.: Tensor renormalization group approach to two-dimensional classical Lattice models. Phys. Rev. Lett. 99, 120601 (2007)

    Article  ADS  Google Scholar 

  9. Bishop, C.M., et al.: Pattern Recognition and Machine Learning. Springer, Berlin (2006)

    MATH  Google Scholar 

  10. Holland, J.L.: Making Vocational Choices: A Theory of Vocational Personalities and Work Environments. Psychological Assessment Resources. Odessa American, Odessa (1997)

    Google Scholar 

  11. Huang, K.Z., Lu, M.W.: Tensor Analysis. Tsinghua University Press, Beijing (2003)

    Google Scholar 

  12. Guo, W., Kotsia, I., Patras, I.: Tensor learning for regression. IEEE Trans. Image Process. 21(2), 816–827 (2012)

    Article  ADS  MathSciNet  Google Scholar 

  13. Molnar, A., Garre-Rubio, J., Pérez-García, D., Schuch, N., Cirac, J.I.: Normal projected entangled pair states generating the same state. J. Phys. 20(11), 113017 (2018)

    Google Scholar 

  14. Liu, W.Y.: Tensor network states algorithm for two-dimensional quantum many-body systems. dissertation, University of Science and Technology of China

  15. Ekert, A.K.: Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett. 67(6), 661 (1991)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

  17. Gottesman, D.: Theory of quantum secret sharing. Phys. Rev. A 61(4), 042311 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  18. Lai, H., Luo, M.X., Xu, Y.J., Pieprzyk, J., Zhang, J., Pan, L., Orgun, M.A.: A quantum secret sharing scheme using orbital angular momentum onto multiple spin states based on Fibonacci compression encoding. Commun. Theor. Phys. 70(4), 384 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  19. Xiao, L., Long, G.L., Deng, F.G., Pan, J.W.: Efficient multiparty quantum-secret-sharing schemes. Phys. Rev. A 69(5), 052307 (2004)

    Article  ADS  Google Scholar 

  20. Hsu, L.Y.: Quantum secret-sharing protocol based on Grover’s algorithm. Phys. Rev. A 68, 022306 (2003)

    Article  ADS  Google Scholar 

  21. Ahmadi, M., Wu, Y.D., Sanders, B.C.: Relativistic (2,3)-threshold quantum secret sharing. Phys. Rev. D 96(6), 065018 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  22. Zhou, Y., Yu, J., Yan, Z., Jia, X., Zhang, J., Xie, C., Peng, K.: Quantum secret sharing among four players using multipartite bound entanglement of an optical field. Phys. Rev. Lett. 121(15), 150502 (2018)

    Article  ADS  Google Scholar 

  23. Lu, H., Zhang, Z., Chen, L.K., Li, Z.D., Liu, C., Li, L., Liu, N.L., Ma, X., Chen, Y.A., Pan, J.W.: Secret sharing of a quantum state. Phys. Rev. Lett. 117(3), 030501 (2016)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

Hong Lai has been supported by the National Natural Science Foundation of China (No. 61702427) and the Fundamental Research Funds for the Central Universities (XDJK2020B027), the Southwest University Research Fund SWU1908043) the Chongqing innovation Project (No. cx2018076). Josef Pieprzyk has been supported by Australian Research Council (ARC) Grant DP180102199 and Polish National Science Center (NCN) Grant 2018/31/B/ST6/03003.

Author information

Authors and Affiliations

  1. School of Computer and Information Science, Southwest University, Chongqing, 400715, China

    Hong Lai

  2. Data61, CSIRO, Sydney, NSW, 2122, Australia

    Josef Pieprzyk

  3. Institute of Computer Science, Polish Academy of Sciences, 01-248, Warsaw, Poland

    Josef Pieprzyk

  4. School of Information Technology, Deakin University, Geelong, VIC, 3220, Australia

    Lei Pan

Authors
  1. Hong Lai
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Josef Pieprzyk
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Lei Pan
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Hong Lai.

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

Lai, H., Pieprzyk, J. & Pan, L. Analysis of weighted quantum secret sharing based on matrix product states. Quantum Inf Process 19, 418 (2020). https://doi.org/10.1007/s11128-020-02925-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-020-02925-w

Keywords