Complementary quantum correlations among multipartite systems | Quantum Information Processing Skip to main content
Springer Nature Link
Log in

Complementary quantum correlations among multipartite systems

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

We study the monogamy and polygamy relations related to quantum correlations for multipartite quantum systems. General monogamy relations are presented for the \(\alpha \)th \((0\le \alpha \le \gamma , \gamma \ge 2)\) power of quantum correlation, and general polygamy relations are given for the \(\beta \)th \((\beta \ge \delta , 0\le \delta \le 1)\) power of quantum correlation. These monogamy and polygamy inequalities are complementary to the existing ones with different parameter regions of \(\alpha \) and \(\beta \). Applying these results to specific quantum correlations, the corresponding new classes of monogamy and polygamy relations are obtained, which include the existing ones as special cases. Detailed examples are given.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
¥17,985 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Japan)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

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

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

  7. Gour, G., Guo, Y.: Monogamy of entanglement without inequalities. Quantum 2, 81 (2018)

    Article  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  9. Jin, Z.X., Fei, S.M.: Tighter monogamy relations of quantum entanglement for multiqubit W-class states. Quantum Inf Process 17, 2 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  10. Jin, Z.X., Fei, S.M., Li-Jost, X.: Improved monogamy relations with concurrence of assistance and negativity of assistance for multiqubit W-class states. Quantum Inf Process 17, 213 (2018)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  14. 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 

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

    Article  ADS  MathSciNet  Google Scholar 

  16. Kim, J.S., Sanders, B.C.: J. Phys. A: Math. Theor. 44, 295303 (2011)

    Article  Google Scholar 

  17. Kalaga, J.K., Leoński, W.: Quantum steering borders in three-qubit systems. Quantum Inf Process 16, 175 (2017)

    Article  ADS  Google Scholar 

  18. Kalaga, J.K., Leoński, W., Szcześniak, R.: Quantum steering and entanglement in three-mode triangle Bose-Hubbard system. Quantum Inf Process 16, 265 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  19. Olsen, M.K.: Spreading of entanglement and steering along small Bose-Hubbard chains. Phys. Rev. A 92, 033627 (2015)

    Article  ADS  Google Scholar 

  20. Deng, X., Xiang, Y., Tian, C., Adesso, G., He, Q.: Demonstration of Monogamy Relations for Einstein-Podolsky-Rosen Steering in Gaussian Cluster States. Phys. Rev. Lett. 118, 230501 (2017)

    Article  ADS  Google Scholar 

  21. Kalaga, J.K., Leoński, W.: Einstein-Podolsky-Rosen steering and coherence in the family of entangled three-qubit states. Phys. Rev. A 97, 042110 (2018)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  23. Laustsen, T., Verstraete, F., van Enk, S.J.: Local vs joint measurements for the entanglement of assistance. Quantum Inf. Comput. 3, 64 (2003)

    MathSciNet  MATH  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  25. Zhu, X.N., Fei, S.M.: Monogamy properties of qubit systems. Quantum Inf Process 18, 23 (2019)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

  27. 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 

  28. Acin, A., Andrianov, A., Costa, L., Jane, E., Latorre, J.I., Tarrach, R.: Generalized schmidt decomposition and classification of three-quantum-bit states. Phys. Rev. Lett. 85, 1560 (2000)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  30. Groblacher, S., Jennewein, T., Vaziri, A., Weihs, G., Zeilinger, A.: Experimental quantum cryptography with qutrits. New J. Phys. 8, 75 (2006)

    Article  ADS  Google Scholar 

  31. Kumar, A., Prabhu, R., Sen(De), A., Sen, U.: Effect of a large number of parties on the monogamy of quantum correlations. Phys. Rev. A 91, 012341 (2015)

  32. Adesso, G., Serafini, A., Illuminati, F.: Multipartite entanglement in three-mode Gaussian states of continuous-variable systems: Quantification, sharing structure, and decoherence. Phys. Rev. A 73, 032345 (2006)

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  34. Prabhu, R., Pati, A.K., Sen(De), A., Sen, U.: Conditions for monogamy of quantum correlations: Greenberger-Horne-Zeilinger versus \(W\) states. Phys. Rev. A 85, 040102(R) (2012)

  35. Giorgi, G.L.: Monogamy properties of quantum and classical correlations. Phys. Rev. A 84, 054301 (2011)

    Article  ADS  Google Scholar 

  36. Salini, K., Prabhu, R., Sen(De), A., Sen, U.: Monotonically increasing functions of any quantum correlation can make all multiparty states monogamous. Ann. Phys 348, 297–305 (2014)

  37. 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)

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  39. Rungta, P., Buz̆ek, 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 

  40. 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 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We thank anonymous reviewers for their suggestions in improving the manuscript. This work was supported in part by the National Natural Science Foundation of China (NSFC) under Grants 11847209; 11675113 and 11635009; the Key Project of Beijing Municipal Commission of Education (Grant No. KZ201810028042); the Beijing Natural Science Foundation (Z190005); the Ministry of Science and Technology of the Peoples’ Republic of China (2015CB856703); the Strategic Priority Research Program of the Chinese Academy of Sciences, Grant No. XDB23030100 and the China Postdoctoral Science Foundation funded project.

Author information

Authors and Affiliations

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

    Zhi-Xiang Jin & Cong-Feng Qiao

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

    Shao-Ming Fei

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

    Shao-Ming Fei

  4. CAS Center for Excellence in Particle Physics, Beijing, 100049, China

    Cong-Feng Qiao

Authors
  1. Zhi-Xiang Jin
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Shao-Ming Fei
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Cong-Feng Qiao
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Zhi-Xiang Jin.

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

Jin, ZX., Fei, SM. & Qiao, CF. Complementary quantum correlations among multipartite systems. Quantum Inf Process 19, 101 (2020). https://doi.org/10.1007/s11128-020-2598-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-020-2598-6