Skip to main content
Log in

The Recurrence Relation of Maximally Six-, Seven- and Eight-Qubit Entangled States

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

The exploration of quantum entanglement in multipartite quantum systems is of great significance to the study of quantum entanglement, maximally multi-qubit entangled state is one of the research objects. Recently, Che et al. presented a recurrence relation of multi-qubit state. According to this inspiration, we present the recurrence relation of maximally multi-qubit pure states of N-qubits for N = 6, 7, 8. Further, some new forms of the seven- and eight-qubit maximally entangled states are found with the recurrence relation.

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.

Similar content being viewed by others

References

  1. Bennett, C.H., Brassard, G., Crépeau, C., et al.: 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 

  2. Deng, F.G., Long, G.L.: Secure direct communication with a quantum one-time pad. Phys. Rev. A 69, 052319 (2004)

    Article  ADS  Google Scholar 

  3. Deng, F.G., Long, G.L.: Controlled order rearrangement encryption for quantum key distribution. Phys. Rev. A 68, 042315 (2003)

    Article  ADS  Google Scholar 

  4. Facchi, P., Florio, G., Parisi, G., et al.: Maximally multipartite entangled states. Phys. Rev. A 77(R), 060304 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  5. Albeverio, S., Fei, S.M., Parashar, P., et al.: Nonlocal properties and local invariants for bipartite systems. Phys. Rev. A 68, 010303 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  6. Borras, A., Plastino, A.R., Batle, J., et al.: Multiqubit systems: highly entangled states and entanglement distribution. Phys. A: Math. Theor 40, 13407 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  7. De Vicente, J.I., Spee, C., Kraus, B.: The maximally entangled set of multipartite quantum states. Phys. Rev. Lett. 111, 110502 (2013)

    Article  Google Scholar 

  8. Goyeneche, D., Bielawski, J., Zyczkowski, K.: Multipartite entanglement in heterogeneous systems. Phys. Rev. A 90, 22316 (2014)

    Article  ADS  Google Scholar 

  9. Yuan, J.P., Dong, S.C., Wu, C.H., et al.: Optically tunable grating in a V plus Xi configuration involving a Rydberg state. Opt. Express 28, 23820 (2020)

    Article  ADS  Google Scholar 

  10. Zhang, Z.Y., Liang, S., Li, F., et al.: Spin-orbit coupling in photonic graphene. Optica 7, 455 (2020)

    Article  ADS  Google Scholar 

  11. Che, J.L., Zhang, Z.Y., Hu, M.L., et al.: Novel Rydberg eight-wave mixing process controlled in the nonlinear phase of a circularly polarized field. Opt. Express 26, 3024 (2018)

    ADS  Google Scholar 

  12. Che, J.L., Wu, H.: Construct multipartite maximally entangled state via recurrence relation. Int. J. Theor. Phys. 58, 584–590 (2019)

    Article  Google Scholar 

  13. Zha, X.W., Yuan, C.Z., Zhang, Y.P.: Generalized criterion for a maximally multi-qubit entangled state. Laser Phys. Lett. 10, 45201 (2013)

    Article  Google Scholar 

  14. Zha, X.W., Song, H.Y., Qi, J.X., et al.: A maximally entangled seven-qubit state. Phys. A Math. Theor 45, 25 (2012)

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work was not supported by any Funding.

Author information

Authors and Affiliations

Authors

Contributions

All authors contributed equally to this research or paper.

Corresponding author

Correspondence to Yi Hu.

Ethics declarations

Conflict of Interests

On behalf of all authors, the corresponding author states that there is 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

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhi, P., Hu, Y. The Recurrence Relation of Maximally Six-, Seven- and Eight-Qubit Entangled States. Int J Theor Phys 60, 2049–2053 (2021). https://doi.org/10.1007/s10773-021-04820-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-021-04820-1

Keywords

Navigation