Skip to main content
SpringerLink
Log in

Separability criteria based on the correlation tensor moments for arbitrary dimensional states

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

As one of the most profound features of quantum mechanics, entanglement is a vital resource for quantum information processing. Inspired by the recent work on PT-moments and separability [Phys. Rev. Lett. 127, 060504 (2021)], we propose two sets of separability criteria using moments of the correlation tensor for bipartite and multipartite quantum states, which are shown to be stronger in some aspects in detecting entanglement.

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

Similar content being viewed by others

Data Availability

All data generated or analyzed during this study are available from the corresponding author on reasonable request.

References

  1. Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)

    Google Scholar 

  2. Bruss, D., Macchiavello, C.: Multipartite entanglement in quantum algorithms. Phys. Rev. A 83, 052313 (2011)

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  CAS  PubMed  Google Scholar 

  4. Schauer, S., Huber, M., Hiesmayr, B.C.: Experimentally feasible security check for n-qubit quantum secret sharing. Phys. Rev. A 82, 062311 (2010)

    Article  ADS  Google Scholar 

  5. Lioyd, S.: Universal quantum simulators. Science 273, 1073 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  6. Gao, T., Yan, F.L., Li, Y.C.: Optimal controlled teleportation. Europhys. Lett. 84, 50001 (2008)

    Article  ADS  Google Scholar 

  7. Zhang, L., Chen, Z., Fei, S.-M.: Entanglement verification with deep semi-supervised machine learning. Phys. Rev. A 108, 022427 (2023)

    Article  ADS  CAS  Google Scholar 

  8. Zhu, X., Wang, J., Bao, G., Li, M., Shen, S.-Q., Fei, S.-M.: A family of bipartite separability criteria based on Bloch representation of density matrices. Quant. Inf. Process. 22, 185 (2023)

    Article  ADS  MathSciNet  Google Scholar 

  9. Li, Y., Shang, J.: Geometric mean of bipartite concurrences as a genuine multipartite entanglement measure. Phys. Rev. Res. 4, 023059 (2022)

    Article  CAS  Google Scholar 

  10. Zangi, S.M., Li, J.-L., Qiao, C.-F.: Quantum state concentration and classification of multipartite entanglement. Phys. Rev. A 97, 012301 (2018)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  11. Rahman, A., Ali, H., Haddadi, S., Zangi, S.M.: Generating non-classical correlations in two-level atoms. Alex. Eng. J. 67, 425 (2023)

    Article  Google Scholar 

  12. Peres, A.: Separability criterion for density matrices. Phys. Rev. Lett. 77, 1413 (1996)

    Article  ADS  MathSciNet  CAS  PubMed  Google Scholar 

  13. Horodecki, M., Horodecki, P., Horodecki, R.: Separability of mixed states: necessary and sufficient conditions. Phys. Lett. A 223, 1 (1996)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  14. Chen, K., Wu, L.A.: A matrix realignment method for recognizing entanglement. Quantum Inf. Comput. 3, 193 (2002)

    ADS  MathSciNet  Google Scholar 

  15. Gühne, O., Hyllus, P., Gittsovich, O., Eisert, J.: Covariance matrices and the separability problem. Phys. Rev. Lett. 99, 130504 (2007)

    Article  ADS  MathSciNet  PubMed  Google Scholar 

  16. Gühne, O., Tóth, G.: Entanglement detection. Phys. Rep. 474, 1 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  17. Elben, A., Kueng, R., Huang, H., Bijnen, R., Kokail, C., Dalmonte, M., Calabrese, P., Kraus, B., Preskill, J., Zoller, P., Vermersch, B.: Mixed-state entanglement from local randomized measurements. Phys. Rev. Lett. 125, 200501 (2020)

    Article  ADS  CAS  PubMed  Google Scholar 

  18. Yu, X., Imai, S., Gühne, O.: Optimal entanglement certification from moments of the partial transpose. Phys. Rev. Lett. 127, 060504 (2021)

    Article  ADS  MathSciNet  CAS  PubMed  Google Scholar 

  19. Zhang, T., Jing, N., Fei, S.-M.: Quantum separability criteria based on realignment moments. Quant. Inf. Process. 21, 276 (2022)

    Article  ADS  MathSciNet  Google Scholar 

  20. Vicente, J.D.: Further results on entanglement detection and quantification from the correlation matrix criterion. J. Phys. A: Math. Theor. 41, 065309 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  21. de Vicente, J.I.: Separability criteria based on the Bloch representation of density matrices. Quantum Inf. Comput. 7, 624 (2007)

    MathSciNet  Google Scholar 

  22. de Vicente, J.I., Huber, M.: Multipartite entanglement detection from correlation tensors. Phys. Rev. A 84, 062306 (2011)

    Article  ADS  Google Scholar 

  23. Sarbicki, G., Scala, G., Chruściński, D.: Family of multipartite separability criteria based on a correlation tensor. Phys. Rev. A 101, 012341 (2020)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  24. Laskowski, W., Markiewicz, M., Paterek, T., Żukowski, M.: Correlation-tensor criteria for genuine multiqubit entanglement. Phys. Rev. A 84, 062305 (2014)

    Article  ADS  Google Scholar 

  25. Li, M., Wang, J., Fei, S.-M., Li-Jost, X.: Quantum separability criteria for arbitrary-dimensional multipartite states. Phys. Rev. A 89, 022325 (2014)

    Article  ADS  Google Scholar 

  26. Shen, S., Yu, J., Li, M., Fei, S.-M.: Improved separability criteria based on Bloch representation of density matrices. Sci. Rep. 6, 28850 (2016)

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  27. Chang, J., Cui, M., Zhang, T., Fei, S.-M.: Separability criteria based on Heisenberg–Weyl representation of density matrices. Chin. Phys. B 27, 030302 (2018)

    Article  ADS  Google Scholar 

  28. Zhao, H., Yang, Y., Jing, N., Wang, Z.X., Fei, S.-M.: Detection of multipartite entanglement based on Heisenberg–Weyl representation of density matrices. Quantum Inf. Process. 19, 1 (2020)

    ADS  Google Scholar 

  29. Zangi, S.M., Qiao, C.-F.: Robustness of entangled states against qubit loss. Phys. Lett. A 400, 127322 (2021)

    Article  MathSciNet  CAS  Google Scholar 

  30. Hassan, A.S.M., Joag, P.S.: Separability criterion for multipartite quantum states based on the Bloch representation of density matrices. Quantum Inf. Comput. 8, 773 (2008)

    MathSciNet  CAS  Google Scholar 

  31. Werner, R.F.: Quantum states with Einstein–Podolsky–Rosen correlations admitting a hidden-variable model. Phys. Rev. A 40, 4277 (1989)

    Article  ADS  CAS  Google Scholar 

  32. Huang, X., Zhang, T., Zhao, M., Jing, N.: Separability criteria based on the Weyl operators. Entropy 24, 1064 (2022)

    Article  ADS  MathSciNet  PubMed  PubMed Central  Google Scholar 

  33. Vicente, J.I.: Further results on entanglement detection and quantification from the correlation matrix criterion. J. Phys. A: Math. Theor. 41, 065309 (2008)

    Article  ADS  MathSciNet  Google Scholar 

Download references

Acknowledgements

The research is partially supported by the Simons Foundation (grant 563828) and the specific research fund of the Innovation Platform for Academicians of Hainan Province under Grant No. YSPTZX202215.

Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, Hainan Normal University, Haikou, 571158, China

    Xiaofen Huang

  2. Key Laboratory of Data Science and Smart Education, Ministry of Education, Hainan Normal University, Haikou, 571158, China

    Xiaofen Huang

  3. Department of Mathematics, North Carolina State University, Raleigh, NC, 27695, USA

    Naihuan Jing

Authors
  1. Xiaofen Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Naihuan Jing
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xiaofen Huang.

Ethics declarations

Conflict of interest

We declare that we 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

Huang, X., Jing, N. Separability criteria based on the correlation tensor moments for arbitrary dimensional states. Quantum Inf Process 23, 53 (2024). https://doi.org/10.1007/s11128-024-04262-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-024-04262-8

Keywords

Search

Navigation