Skip to main content
SpringerLink
Log in

Polygamy Inequalities for Qubit Systems

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

Abstract

Entanglement polygamy, like entanglement monogamy, is a fundamental property of multipartite quantum states. We investigate the polygamy relations related to the concurrence C and the entanglement of formation E for general n-qubit states. We extend the results in [Phys. Rev. A 90, 024304 (2014)] from the parameter region α ≤ 0 to α ≤ α0, where 0 < α0 ≤ 2 for C, and \(0<\alpha _{0}\leq \sqrt {2}\) for E.

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
Fig. 4

Similar content being viewed by others

References

  1. Mintert, F., Kuś, M., Buchleitner, A.: Concurrence of mixed bipartite quantum states in arbitrary dimensions. Phys. Rev. Lett. 92, 167902 (2004)

    Article  ADS  Google Scholar 

  2. Chen, K., Albeverio, S., Fei, S.M.: Concurrence of arbitrary dimensional bipartite quantum states. Phys. Rev. Lett. 95, 040504 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  3. Breuer, H.P.: Optimal entanglement criterion for mixed quantum states. Phys. Rev. Lett. 97, 080501 (2006)

    Article  ADS  Google Scholar 

  4. de Vicente, J.I.: Lower bounds on concurrence and separability conditions. Phys. Rev. A 75, 052320 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  5. Zhang, C.J., Zhang, Y.S., Zhang, S., Guo, G.C.: Optimal entanglement witnesses based on local orthogonal observables. Phys. Rev. A 76, 012334 (2007)

    Article  ADS  Google Scholar 

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

    MATH  Google Scholar 

  7. Pawlowski, M.: Security proof for cryptographic protocols based only on the monogamy of Bell’s inequality violations. Phys. Rev. A 82, 032313 (2010)

    Article  ADS  Google Scholar 

  8. Koashi, M., Winter, A.: Monogamy of quantum entanglement and other correlations. Phys. Rev. A 69, 022309 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  9. Guo, Y.: Any entanglement of assistance is polygamous. Quantum Inf. Process 17, 222 (2018)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  10. Osborne, T.J., Verstraete, F.: General monogamy inequality for bipartite qubit entanglement. Phys. Rev. Lett. 96, 220503 (2006)

    Article  ADS  Google Scholar 

  11. Bai, Y.K., Ye, M.Y., Wang, Z.D.: Entanglement monogamy and entanglement evolution in multipartite systems. Phys. Rev. A 80, 044301 (2009)

    Article  ADS  Google Scholar 

  12. Bai, Y.K., Xu, Y.F., Wang, Z.D.: General monogamy relation for the entanglement of formation in multiqubit systems. Phys. Rev. Lett. 113, 100503 (2014)

    Article  ADS  Google Scholar 

  13. Coffman, V., Kundu, J., Wootters, W.K.: Distributed entanglement. Phys. Rev. A 61, 052306 (2000)

    Article  ADS  Google Scholar 

  14. Zhu, X.N., Fei, S.M.: Entanglement monogamy relations of qubit systems, Entanglement monogamy relations of qubit systems. Phys. Rev. A 90, 024304 (2014)

    Article  ADS  Google Scholar 

  15. Jin, Z.X., Li, J., Li, T., Fei, S.M.: Tighter monogamy relations in multiqubit systems, Tighter monogamy relations in multiqubit systems. Phys. Rev. A 97, 032336 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  16. Kim, J.S.: Negativity and tight constraints of multiqubit entanglement. Phys. Rev. A 97, 012334 (2018)

    Article  ADS  Google Scholar 

  17. Goura, G., Bandyopadhyayb, S., Sandersc, B.C.: . J. Math. Phys. 48, 012108 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  18. Kim, J.S.: Weighted polygamy inequalities of multiparty entanglement in arbitrary-dimensional quantum systems. Phys. Rev. A 97, 042332 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  19. Uhlmann, A.: Fidelity and concurrence of conjugated states. Phys. Rev. A 62, 032307 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  20. Rungta, P., Bužek, V., Caves, C.M., Hillery, M., Milburn, G.J.: Universal state inversion and concurrence in arbitrary dimensions. Phys. Rev. A 64, 042315 (2001)

    Article  ADS  MathSciNet  Google Scholar 

  21. Albeverio, S., Fei, S.M.: A note on invariants and entanglements. J Opt B: Quantum Semiclass Opt. 3, 223 (2001)

    Article  ADS  MathSciNet  Google Scholar 

  22. Yu, C.S., Song, H.S.: Entanglement monogamy of tripartite quantum states. Phys. Rev. A 77, 032329 (2008)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  23. Bennett, C.H., Bernstein, H.J., Popescu, S., Schumacher, B.: Concentrating partial entanglement by local operations. Phys. Rev. A 53, 2046 (1996)

    Article  ADS  Google Scholar 

  24. Bennett, C.H., DiVincenzo, D.P., Smolin, J.A., Wootters, W.K.: Mixed-state entanglement and quantum error correction. Phys. Rev. A 54, 3824 (1996)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  25. Kim, J.S.: General polygamy inequality of multiparty quantum entanglement. Phys. Rev. A 85, 062302 (2012)

    Article  ADS  Google Scholar 

Download references

Acknowledgments

This work is supported by NSFC under numbers 11675113, 11605083, and Beijing Municipal Commission of Education (KZ201810028042).

Author information

Authors and Affiliations

  1. School of Mathematics and Statistics Science, Ludong University, Yantai, 264025, China

    Xue-Na Zhu

  2. School of Physics, University of Chinese Academy of Sciences, Yuquan Road 19A, Beijing, 100049, China

    Zhi-Xiang Jin

  3. School of Mathematical Sciences, Capital Normal University, Beijing, 100048, China

    Shao-Ming Fei

  4. Max-Planck-Institute for Mathematics in the Sciences, 04103, Leipzig, Germany

    Shao-Ming Fei

Authors
  1. Xue-Na Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhi-Xiang Jin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Shao-Ming Fei
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xue-Na Zhu.

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

Zhu, XN., Jin, ZX. & Fei, SM. Polygamy Inequalities for Qubit Systems. Int J Theor Phys 58, 2488–2496 (2019). https://doi.org/10.1007/s10773-019-04139-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-019-04139-y

Keywords

Search

Navigation