Skip to main content
SpringerLink
Log in

Enhanced Monogamy Relations in Multiqubit Systems

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

Abstract

We investigate the monogamy relations of multipartite entanglement in terms of the α th power of concurrence, entanglement of formation, negativity and Tsallis-q entanglement. Enhanced new monogamy relations of multipartite entanglement with tighter lower bounds than the existing monogamy relations are presented, together with detailed examples showing the tightness. These monogamy relations give rise to finer characterization of the entanglement distributions among the subsystems of a multipartite 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

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. Terhal, B.M.: Is entanglement monogamous? IBM J. Res. Dev. 48, 71 (2004)

    Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  MathSciNet  Google Scholar 

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

    ADS  Google Scholar 

  5. Ou, Y.C., Fan, H.: Monogamy inequality in terms of negativity for three-qubit states. Phys. Rev. A. 75, 062308 (2007)

    ADS  MathSciNet  Google Scholar 

  6. Kim, J.S., Das, A., Sanders, B.C.: Entanglement monogamy of multipartite higher-dimensional quantum systems using convex-roof extend negativity. Phys. Rev. A. 79, 012329 (2009)

    ADS  Google Scholar 

  7. Streltsov, A., Adesso, G., Piani, M., Bruß, D.: Are general quantum correlations monogamous? Phys. Rev. Lett. 109, 050503 (2012)

    ADS  Google Scholar 

  8. 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)

    ADS  Google Scholar 

  9. Song, W., Bai, Y.K., Yang, M., Cao, Z.L.: General monogamy relation of multiqubit systems in terms of squared rényi-a entanglement. Phys. Rev. A. 93, 022306 (2016)

    ADS  MathSciNet  Google Scholar 

  10. Luo, Y., Tian, T., Shao, L.H., Li, Y.: General monogamy of Tsallis-q entropy entanglement in multiqubit systems. Phys. Rev. A. 93, 062340 (2016)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  12. Ma, X., Dakic, B., Naylor, W., Zeilinger, A., Walther, P.: Quantum simulation of the wavefunction to probe frustrated Heisenberg spin systems. Nat. Phys. 7, 399 (2011)

    Google Scholar 

  13. Pawłowski, M., Brukner, C̆.: Monogamy of Bell’s inequality violations in nonsignaling theories. Phys. Rev. Lett. 102, 030403 (2009)

    ADS  MathSciNet  Google Scholar 

  14. Seevinck, M.P.: Monogamy of correlations versus monogamy of entanglement. Quantum Inf. Process. 9, 273 (2010)

    MathSciNet  MATH  Google Scholar 

  15. Verlinde, E., Verlinde, H.: Black hole entanglement and quantum error correction. J. High Energy Phys. 1310, 107 (2013)

    ADS  MathSciNet  MATH  Google Scholar 

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

    ADS  MathSciNet  Google Scholar 

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

    ADS  Google Scholar 

  18. Jin, Z.X., Fei, S.M.: Tighter entanglement monogamy relations of qubit systems. Quantum Inf. Process. 16, 77 (2017)

    ADS  MathSciNet  MATH  Google Scholar 

  19. Kim, J.S., Sanders, B.C.: Monogamy of multi-qubit entanglement using rényi entropy. J. Phys. A: Math. Theor. 43, 445305 (2010)

    MATH  Google Scholar 

  20. Kim, J.S.: Tsallis entropy and entanglement constraints in multiqubit systems. Phys. Rev A. 81, 062328 (2010)

    ADS  MathSciNet  Google Scholar 

  21. Kim, J.S.: Generalized entanglement constraints in multi-qubit systems in terms of Tsallis entropy. Ann. Phys. 373, 197 (2016)

    ADS  MathSciNet  MATH  Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  MathSciNet  Google Scholar 

  24. Gour, G., Bandyopadhay, S., Sanders, B.C.: Dual monogamy inequality for entanglement. J. Math. Phys. 48, 012108 (2007)

    ADS  MathSciNet  MATH  Google Scholar 

  25. Yang, L.M., Chen, B., Fei, S.M., Wang, Z.X.: Tighter constraints of multi-qubit entanglement. Commun. Theor. Phys. 71, 545 (2019)

    ADS  MathSciNet  Google Scholar 

  26. Buscemi, F., Gour, G., Kim, J.S.: Polygamy of distributed entanglement. Phys. Rev. A. 80, 012324 (2009)

    ADS  Google Scholar 

  27. Jin, Z.X., Fei, S.M.: Finer distribution of quantum correlations among multiqubit systems. Quantum Inf. Process. 18, 21 (2019)

    ADS  MathSciNet  MATH  Google Scholar 

  28. Jin, Z.X., Fei, S.M.: Superactivation of monogamy relations for nonadditive quantum correlation measures. Phys. Rev. A. 99, 032343 (2019)

    ADS  Google Scholar 

  29. Gour, G., Meyer, D.A., Sanders, B.C.: Deterministic entanglement of assistance and monogamy constraints. Phys. Rev. A. 72, 042329 (2005)

    ADS  Google Scholar 

  30. Wootters, W.K.: Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett. 80, 2245 (1998)

    ADS  MATH  Google Scholar 

  31. Gao, L.M., Yan, F.L., Gao, T.: Tighter monogamy relations of multiqubit entanglement in terms of Ré,nyi-a entanglement. arXiv:1905.02952(2019)

  32. Ren, X.J., Jiang, W.: Entanglement monogamy inequality in a 2 ⊗ 2 ⊗ 4 system. Phys. Rev. A. 81, 024305 (2010)

    ADS  Google Scholar 

  33. Acin, A., Andrianov, A., Costa, L., Jané, E., Latorre, J.I., Tarrach, R.: Generalized schmidt decomposition and classification of Three-Quantum-Bit states. Phys. Rev. Lett. 85, 1560 (2000)

    ADS  Google Scholar 

  34. Gao, X.H., Fei, S.M.: Estimation of concurrence for multipartite mixed states. Eur. Phys. J. Special Topics. 159, 71–77 (2008)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  36. 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)

    ADS  MathSciNet  MATH  Google Scholar 

  37. Bai, Y.K., Zhang, N., Ye, M.Y., Wang, Z.D.: Exploring multipartite quantum correlations with the square of quantum discord. Phys. Rev. A. 88, 012123 (2013)

    ADS  Google Scholar 

  38. Vidal, G., Werner, R.F.: Computable measure of entanglement. Phys. Rev. A 65, 032314 (2002)

    ADS  Google Scholar 

  39. Horodeki, P.: Separability criterion and inseparable mixed states with positive partial transposition. Phys. Lett. A. 232, 333 (1997)

    ADS  MathSciNet  MATH  Google Scholar 

  40. Dür, W., Cirac, J.I., Lewenstein, M., Bruß, D.: Distillability and partial transposition in bipartite systems. Phys. Rev. A. 61, 062313 (2000)

    ADS  MathSciNet  Google Scholar 

  41. Tsallis, C.: Possible generalization of Boltzmann-Gibbs statistics. J. Stat. Phys. 52, 479 (1988)

    ADS  MathSciNet  MATH  Google Scholar 

  42. Landsberg, P.T., Vedral, V.: Distributions and channel capacities in generalized statistical mechanics. Phys. Lett. A. 247, 211 (1998)

    ADS  MathSciNet  MATH  Google Scholar 

  43. Rajagopal, A.K., Rendell, R.W.: Classical statistics inherent in a quantum density matrix. Phys. Rev. A. 72, 022322 (2005)

    ADS  Google Scholar 

  44. Yuan, G.M., Song, W., Yang, M., Li, D.C., Zhao, J.L., Cao, Z.L.: Monogamy relation of multi-qubit systems for squared Tsallis-q entanglement. Sci. Rep. 6, 28719 (2016)

    ADS  Google Scholar 

Download references

Acknowledgments

This work is supported by the Natural Science Foundation of China (NSFC) under Grants No. 11847209 and No. 11675113, Key Project of Beijing Municipal Commission of Education under Grant No. KZ201810028042, Beijing Natural Science Foundation under Grant No. Z190005, China Postdoctoral Science Foundation funded project No. 2019M650811, the China Scholarship Council No. 201904910005, Academy for Multidisciplinary Studies, Capital Normal University, and Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China (No. SIQSE202001).

Author information

Authors and Affiliations

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

    Jiabin Zhang, Shao-Ming Fei & Zhi-Xi Wang

  2. School of Information, Beijing Wuzi University, Beijing, 101149, China

    Jiabin Zhang

  3. School of Physics, University of Chinese Academy of Sciences, Beijing, 100049, China

    Zhixiang Jin

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

    Shao-Ming Fei

Authors
  1. Jiabin Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhixiang 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

  4. Zhi-Xi Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jiabin Zhang.

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

Zhang, J., Jin, Z., Fei, SM. et al. Enhanced Monogamy Relations in Multiqubit Systems. Int J Theor Phys 59, 3449–3463 (2020). https://doi.org/10.1007/s10773-020-04603-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-020-04603-0

Keywords

Search

Navigation