Skip to main content
SpringerLink
Log in

Local Unitary Invariants of Quantum States

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

Abstract

We study the equivalence of mixed states under local unitary transformations. First we express quantum states in Bloch representation. Then based on the coefficient matrices, some invariants are constructed. This method and results can be extended to multipartite high dimensional system.

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

References

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

  2. Duer, W., Vidal, G., Cirac, J.I.: Phys. Rev. A 62, 062314 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  3. Carteret, H.A., Higuchi, A., Sudbery, A.: J. Math. Phys. 41, 7932 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  4. Verstraete, F., Dehaene, J., Moor, B.D.: Phys. Rev. A 68, 012103 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  5. Kraus, B.: Phys. Rev. Lett. 104, 020504 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  6. Kraus, B.: Phys. Rev. A 82, 032121 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  7. Liu, B., Li, J.-L., Li, X., Qiao, C.-F.: Phys. Rev. Lett 108, 050501 (2012)

    Article  ADS  Google Scholar 

  8. Zhang, T.G., Zhao, M.J., Li, M., Fei, S.M., Li-Jost, X.: Phys. Rev. A 88, 042304 (2013)

    Article  ADS  Google Scholar 

  9. Giedke, G., Kraus, B.: Phys. Rev. A 89, 012335 (2014)

    Article  ADS  Google Scholar 

  10. Li, M., Zhang, T., Fei, S.M., Li-Jost, X., Jing, N.: Phys. Rev. A 89, 062325 (2014)

    Article  ADS  Google Scholar 

  11. Zhang, T., Hua, B., Li, M., Zhao, M.J., Yang, H.: Chin. Phys. B 24, 120305 (2015)

    Article  ADS  Google Scholar 

  12. Tsimakuridze, N., Gühne, O.: arXiv:1611.06938 (2016)

  13. Makhlin, Y.: Quan. Inf. Pro 1, 243 (2002)

    Article  MathSciNet  Google Scholar 

  14. Linden, N., Popescu, S., Sudbery, A.: Phys. Rev. Lett. 83, 243 (1999)

    Article  ADS  Google Scholar 

  15. Sun, B.Z., Fei, S.M.: Commun. Theor. Phys. 45, 1007 (2006)

    Article  ADS  Google Scholar 

  16. Sun, B.Z., Fei, S.M., Li-Jost, X.Q., Wang, Z.X.: J. Phys. A: Math. Gen. 39, L43 (2006)

    Article  Google Scholar 

  17. Albeverio, S., Fei, S.M., Parashar, P., Yang, W.L.: Phys. Rev. A 68 (R), 010303 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  18. Albeverio, S., Fei, S.M., Goswami, D.: Phys. Lett. A 340, 37–42 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  19. Zhou, C., Zhang, T.G., Fei, S.M., Jing, N., Li-Jost, X.: Phys. Rev. A 86(R), 010303 (2012)

    Article  ADS  Google Scholar 

  20. Martins, A.M.: Phys. Rev. A 91, 042308 (2015)

    Article  ADS  Google Scholar 

  21. Jing, N., Fei, S.M., Li, M., Li-Jost, X., Zhang, T.: Phys. Rev. A 92, 022306 (2015)

    Article  ADS  Google Scholar 

Download references

Acknowledgments

The work is partly supported by the NSF of China under Grant No. 11501153, No. 11401032 and No. 11661031; the NSF of Hainan Province under Grant No. 20161006 and the project of the Education Department of Hainan Province under Grant No. Hnky2015-18.

Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, Hainan Normal University, Haikou, 571158, People’s Republic of China

    Meiyu Cui, Jingmei Chang, Xiaofen Huang & Tinggui Zhang

  2. School of Science, Beijing Information Science and Technology University, 100192, Beijing, China

    Ming-Jing Zhao

  3. Hainan Center for Mathematical Research, Hainan Normal University, Haikou, 571158, People’s Republic of China

    Xiaofen Huang & Tinggui Zhang

Authors
  1. Meiyu Cui
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jingmei Chang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ming-Jing Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xiaofen Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Tinggui Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tinggui Zhang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cui, M., Chang, J., Zhao, MJ. et al. Local Unitary Invariants of Quantum States. Int J Theor Phys 56, 3579–3587 (2017). https://doi.org/10.1007/s10773-017-3523-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-017-3523-3

Keywords

Search

Navigation