Skip to main content
SpringerLink
Log in

Hierarchical quantum information splitting of an arbitrary m-qudit state with multiparty

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

In this paper, we concern on different methods to realize hierarchical quantum information splitting of an arbitrary m-qudit state with multiple agents. Two deterministic universal solutions are proposed with the aid of the symmetry feature of cluster state. There exists a hierarchy among the agents in terms of their abilities which are quantified by nonconditioned fidelity. The upper-grade agent needs the assistance of all the remaining upper-grade agents and any one of the lower-grade agents, while the lower-grade agent needs all the other agents’ collaboration. It is worth mentioning that the recovery operation is derived by a general expression which clearly discloses the relationship with the measurement results. Moreover, we consider the effect of two-type high-dimensional decoherence noises.

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

Data availability

Data sharing is not applicable to this article as no datasets were generated or analyzed during the current study

References

  1. Kwek, L.C., Cao, L., Luo, W., Wang, Y.X., Sun, S.H., Wang, X.B., Liu, A.Q.: Chip-based quantum key distribution. AAPPS Bull. 31, 15 (2021)

    ADS  Google Scholar 

  2. Yan, Y.F., Zhou, L., Zhong, W., Sheng, Y.B.: Measurement-device-independent quantum key distribution of multiple degrees of freedom of a single photon. Front. Phys. 16, 11501 (2021)

    ADS  Google Scholar 

  3. Gu, J., Cao, X.Y., Fu, Y., He, Z.W., Yin, Z.J., Yin, H., Yin, H.L., Chen, Z.B.: Experimental measurement-device-independent type quantum key distribution with flawed and correlated sources. Sci. Bull. 67, 2167–2175 (2022)

    Google Scholar 

  4. Xie, Y.M., Lu, Y.S., Weng, C.X., Cao, X.Y., Jia, Z.Y., Bao, Y., Wang, Y., Fu, Y., Yin, H.L., Chen, Z.B.: Breaking the rate-loss bound of quantum key distribution with asynchronous two-photon interference. PRX Quantum 3, 020315 (2022)

    ADS  Google Scholar 

  5. Li, Z.J., Wei, K.J.: Improving parameter optimization in decoy-state quantum key distribution. Quantum Eng. 4, 9717591 (2022)

    Google Scholar 

  6. Liu, B., Xia, S., Xiao, D., Huang, W., Xu, B.J., Li, Y.: Decoy-state method for quantum-key-distribution-based quantum private query. Sci. China Phys. Mech. Astron. 65, 240312 (2022)

    ADS  Google Scholar 

  7. Banerjee, A., Pathak, A.: Maximally efficient protocols for direct secure quantum communication. Phys. Lett. A 376, 2944–2950 (2012)

    ADS  Google Scholar 

  8. Zou, Z.K., Zhou, L., Zhong, W., Sheng, Y.B.: Measurement-device-independent quantum secure direct communication of multiple degrees of freedom of a single photon. EPL 131, 40005 (2020)

    ADS  Google Scholar 

  9. Sheng, Y.B., Zhou, L., Long, G.L.: One-step quantum secure direct communication. Sci. Bull. 67, 367–374 (2022)

    Google Scholar 

  10. Zhou, L., Sheng, Y.B.: One-step device-independent quantum secure direct communication. Sci. China Phys. Mech. Astron. 65, 250311 (2022)

    ADS  Google Scholar 

  11. Liu, X., Luo, D., Lin, G.S., Chen, Z.H., Huang, C.F., Li, S.Z., Zhang, C.X., Zhang, Z.R., Wei, K.J.: Fiber-based quantum secure direct communication without active polarization compensation. Sci. China Phys. Mech. Astron. 65, 120311 (2022)

    ADS  Google Scholar 

  12. Li, M.S., Wang, Y.L.: Masking quantum information in multipartite scenario. Phys. Rev. A 98, 062306 (2018)

    ADS  Google Scholar 

  13. Shen, Y., Zhang, F.L., Chen, Y.Z., Zhou, C.C.: Masking quantum information in the Kitaev Abelian anyons. Phys. A 612, 128495 (2023)

    MathSciNet  MATH  Google Scholar 

  14. Hillery, M., Buzek, V., Berthiaume, A.: Quantum secret sharing. Phys. Rev. A 59, 1829–1834 (1999)

    ADS  MathSciNet  MATH  Google Scholar 

  15. Hu, W.W., Zhou, R.G., Li, X., Fan, P., Tan, C.Y.: A novel dynamic quantum secret sharing in high-dimensionalquantum system. Quantum Inf. Process. 20, 159 (2021)

    ADS  MATH  Google Scholar 

  16. Gu, J., Cao, X.Y., Yin, H.L., Chen, Z.B.: Differential phase shift quantum secret sharing using a twin field. Opt. Express 29, 9165–9173 (2021)

    ADS  Google Scholar 

  17. Ahlswede, R., Csiszar, I.: Common randomness in information theory and cryptography. IEEE Trans. Inf. Theor. 39, 1121–1132 (1993)

    MathSciNet  MATH  Google Scholar 

  18. Fu, Y., Yin, H.L., Chen, T.Y., Chen, Z.B.: Long-distance measurement-device-independent multiparty quantum communication. Phys. Rev. Lett. 114, 090501 (2015)

    ADS  Google Scholar 

  19. 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)

    ADS  MathSciNet  MATH  Google Scholar 

  20. Wiesner, S.: Conjugate coding. ACM Sigact News 15, 78–88 (1983)

  21. Lipinska, V., Ribeiro, J., Wehner, S.: Secure multiparty quantum computation with few qubits. Phys. Rev. A 102, 022405 (2022)

    ADS  MathSciNet  Google Scholar 

  22. Hou, K., Liu, G.H., Zhang, X.Y., Sheng, S.Q.: An efficient scheme for five-party quantum state sharing of an arbitrary \(m\)-qubit state using multiqubit cluster states. Quantum Inf. Process. 10, 463–473 (2011)

    MathSciNet  MATH  Google Scholar 

  23. Luo, M.X., Deng, Y.: Quantum splitting an arbitrary three-qubit state with \(\chi \)-state. Quantum Inf. Process. 12, 773–784 (2013)

    ADS  MathSciNet  MATH  Google Scholar 

  24. Li, H.J., Li, J., Xiang, N., Zheng, Y., Yang, Y.G., Naseri, M.: A new kind of universal and flexible quantum information splitting scheme with multi-coin quantum walks. Quantum Inf. Process. 18, 316 (2019)

    ADS  MathSciNet  MATH  Google Scholar 

  25. Lai, H., Pieprzyk, J., Pan, L., Orgun, M.A.: Two types of dynamic quantum state secret sharing based on tensor networks states. Phys. A 582, 126257 (2021)

    MathSciNet  MATH  Google Scholar 

  26. Xu, G., Zhou, T.A., Chen, X.B., Wang, X.J.: Splitting an arbitrary three-qubit state via a five-qubit cluster state and a Bell state. Entropy 24, 381 (2022)

    ADS  MathSciNet  Google Scholar 

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

    ADS  Google Scholar 

  28. Lee, S.M., Lee, S.W., Jeong, H., Park, H.S.: Quantum teleportation of shared quantum secret. Phys. Rev. Lett. 124, 060501 (2020)

    ADS  MathSciNet  Google Scholar 

  29. Wang, X.W., Xia, L.X., Wang, Z.Y., Zhang, D.Y.: Hierarchical quantum information splitting. Opt. Commun. 283, 1196–1199 (2010)

    ADS  Google Scholar 

  30. Wotters, W.K., Zurek, W.H.: A single quantum cannot be clone. Nature 299, 802–803 (1982)

    ADS  Google Scholar 

  31. Wang, X.W., Zhang, D.Y., Tang, S.Q.: Multiparty hierarchical quantum information splitting. J. Phys. B At. Mol. Opt. Phys 44, 035505 (2011)

    ADS  Google Scholar 

  32. Xu, G., Wang, C., Yang, Y.X.: Hierarchical quantum information splitting of an arbitrary two-qubit state via the cluster state. Quantum Inf. Process. 13, 43–57 (2014)

    ADS  MATH  Google Scholar 

  33. Zha, X.W., Miao, N., Wang, H.F.: Hierarchical Quantum information splitting of an arbitrary two-qubit using a single quantum resource. Int. J. Theor. Phys. 58, 2428–2434 (2019)

    MathSciNet  MATH  Google Scholar 

  34. Wang, N.N., Ma, S.Y., Li, X.: Hierarchical controlled quantum communication via the \(\chi \) state under noisy environment. Mod. Phys. Lett. A 60, 2050306 (2020)

    MathSciNet  MATH  Google Scholar 

  35. Tang, J., Ma, S.Y., Li, Q.: Universal hierarchical quantum information splitting schemes of an arbitrary multi-qubit state. Int. J. Theor. Phys. 61, 209 (2022)

    MathSciNet  MATH  Google Scholar 

  36. Guo, W.M., Qin, L.R.: Hierarchical and probabilistic quantum information splitting of an arbitrary two-qubit state via two cluster states. Chin. Phys. B 27, 110302 (2018)

    ADS  Google Scholar 

  37. Xu, G., Shan, R.T., Chen, X.B.: Probabilistic and hierarchical quantum information splitting based on the non-maximally entangled cluster state. Comput. Mat. Continua. 69, 339–349 (2021)

    Google Scholar 

  38. Tang, J., Ma, S.Y., Li, Q.: Probabilistic hierarchical quantum information splitting of arbitrary multi-qubit states. Entropy 24, 1077 (2022)

    MathSciNet  Google Scholar 

  39. Feng, K.H., Lu, X.Q., Zhou, P.: Probabilistic hierarchically controlled teleportation of an arbitrary \(m\)-qudit state with a pure entangled quantum channel. Sci. Sin.-Phys. Mech. Astron. (in Chinese) 52, 230311 (2022)

    Google Scholar 

  40. Cao, T.B., An, N.B.: Hierarchically controlling quantum teleportations. Quantum Inf. Process. 18, 245 (2019)

    ADS  MathSciNet  MATH  Google Scholar 

  41. Cozzolino, D., Da Lio, B., Bacco, D., Oxenlowe, L.K.: High-dimensional quantum communication: benefits, progress, and future challenges. Adv. Quantum Technol. 2, 1900038 (2019)

    Google Scholar 

  42. Li, Q., Ma, S.Y., Tang, J.: Hierarchical remote preparation of arbitrary dimensional equatorial states. Mod. Phys. Lett. A 37, 25 (2022)

    MathSciNet  Google Scholar 

  43. Jin, R.H., Wei, W.S., Zhou, P.: Hierarchical controlled remote preparation of an arbitrary \(m\)-qudit state with four-qudit cluster states. Quantum Inf. Process. 22, 113 (2023)

    ADS  MathSciNet  MATH  Google Scholar 

  44. Luo, M.X.: Nonsignaling causal hierachy of general multisource networks. Phys. Rev. A 101, 062317 (2020)

    ADS  MathSciNet  Google Scholar 

  45. Zhou, N.R., Zhang, T.F., Xie, X.W., Wu, J.Y.: Hybrid quantum-classical generative adversarial networks for image generation via learning discrete distribution. Signal Process. Image Commun 110, 116891 (2023)

    Google Scholar 

  46. Li, X.H., Ghose, S.: Control power in perfect controlled teleportation via partially entangled channels. Phys. Rev. A 90, 052305 (2014)

    ADS  Google Scholar 

  47. Duan, W.X., Wang, T.J.: Control power of high-dimensional controlled dense coding. Phys. Rev. A 105, 052417 (2022)

    ADS  MathSciNet  Google Scholar 

  48. Hein, M., Dür, W., Briegel, H.J.: Entanglement properties of multipartite entangled states under the infuence of decoherence. Phys. Rev. 71, 032350 (2005)

  49. Dong, P., Xue, Z.Y., Yang, M., Cao, Z.L.: Generation of cluster states. Phys. Rev. 73, 033818 (2006)

  50. Qu, Z.G., Liu, X.Z., Sun, L.: Learnable antinoise-receiver algorithm based on a quantum feedforward neural network in optical quantum communication. Phys. Rev. 105, 052427 (2022)

  51. Yan, P.S., Zhou, L., Zhong, W., Sheng, Y.B.: Advances in quantum entanglement purification. Sci. China Phys. Mech. 66, 250301 (2023)

    Google Scholar 

  52. Babazadeh, A., Erhard, M., Wang, F., Malik, M., Nouroozi, R., Krenn, M., Zeilinger, A.: High-dimensional single-photon quantum gates: concepts and experiments. Phys. Rev. A 119, 180510 (2017)

    Google Scholar 

  53. De Oliveira, M., Nape, I., Pinnell, J., TabeBordbar, N., Forbes, A.: Experimental high-dimensional quantum secret sharing with spin-orbit-structured photons. Phys. Rev. A 101, 042303 (2020)

    ADS  Google Scholar 

Download references

Acknowledgements

This work is supported by the National Natural Science Foundation of China (Nos. 61201253, 62172341, 62172196, 62272208).

Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, Henan University, Kaifeng, 475004, China

    Songya Ma, Junli Jiang & Xia Yan

  2. Institute of Mathematics, Henan Academy of Sciences, Zhengzhou, 450046, China

    Songya Ma

Authors
  1. Songya Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Junli Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xia Yan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Songya Ma.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

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 (e.g. a society or other partner) 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

Ma, S., Jiang, J. & Yan, X. Hierarchical quantum information splitting of an arbitrary m-qudit state with multiparty. Quantum Inf Process 22, 263 (2023). https://doi.org/10.1007/s11128-023-04018-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-023-04018-w

Keywords

Search

Navigation