Skip to main content
SpringerLink
Log in

A lower bound of concurrence for multipartite quantum systems

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

We present a lower bound of concurrence for four-partite systems in terms of the concurrence for \(M\, (2\le M\le 3)\) part quantum systems and give an analytical lower bound for \(2\otimes 2\otimes 2\otimes 2\) mixed quantum sates. It is shown that these lower bounds are able to improve the existing bounds and detect entanglement better. Furthermore, our approach can be generalized to multipartite quantum systems.

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

Similar content being viewed by others

References

  1. Horodecki, R., Horodecki, P., Horodecki, M., Horodecki, K.: Quantum entanglement. Rev. Mod. Phys. 81(865), 867–942 (2009)

    ADS  MathSciNet  MATH  Google Scholar 

  2. Wootters, W.K.: Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett. 80(2245), 2245–2248 (1998)

    Article  ADS  MATH  Google Scholar 

  3. Qi, X.F., Gao, T., Yan, F.L.: Lower bounds of concurrence for N-qubit systems and the detection of k-nonseparability of multipartite quantum systems. Quantum Inf. Process. 16(23), 1–8 (2017)

    MathSciNet  MATH  Google Scholar 

  4. Uhlmann, A.: Fidelity and concurrence of conjugated states. Phys. Rev. A 62(032307), 1–9 (2000)

    MathSciNet  Google Scholar 

  5. 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), 1–13 (2001)

    MathSciNet  Google Scholar 

  6. Albeverio, S., Fei, S.M.: A note on invariants and entanglements. J. Opt. B Quantum Semiclass. Opt. 3(223), 1–11 (2001)

    MathSciNet  Google Scholar 

  7. Mintert, F., Kuś, M., Buchleitner, A.: Concurrence of mixed bipartite quantum states in arbitrary dimensions. Phys. Rev. Lett. 92(167902), 1–4 (2004)

    Google Scholar 

  8. Chen, K., Albeverio, S., Fei, S.M.: Concurrence of arbitrary dimensional bipartite quantum states. Phys. Rev. Lett. 95(040504), 1–4 (2005)

    MathSciNet  Google Scholar 

  9. Breuer, H.P.: Separability criteria and bounds for entanglement measures. J. Phys. A Math. Gen. 39(11847), 1–8 (2006)

    MathSciNet  MATH  Google Scholar 

  10. Breuer, H.P.: Optimal entanglement criterion for mixed quantum states. Phys. Rev. Lett. 97(080501), 1–4 (2006)

    Google Scholar 

  11. de Vicente, J.I.: Lower bounds on concurrence and separability conditions. Phys. Rev. A 75(052320), 1–5 (2007)

    MathSciNet  Google Scholar 

  12. Zhang, C.J., Zhang, Y.S., Zhang, S., Guo, G.C.: Optimal entanglement witnesses based on local orthogonal observables. Phys. Rev. A 76(012334), 1–6 (2007)

    Google Scholar 

  13. Zhao, M.J., Zhu, X.N., Fei, S.M.: Lower bound on concurrence and distillation for arbitrary-dimensional bipartite quantum states. Phys. Rev. A 84(062322), 1–5 (2011)

    Google Scholar 

  14. Zhu, X.N., Fei, S.M.: Lower bound of concurrence for qubit systems. Quantum Inf. Process. 13, 815–823 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  15. Zhu, X.N., Zhao, M.J., Fei, S.M.: Lower bound of multipartite concurrence based on subquantum state decomposition. Phys. Rev. A 86(022307), 1–4 (2012)

    Google Scholar 

  16. Carvalho, A.R.R., Mintert, F., Buchleitner, A.: Decoherence and multipartite entanglement. Phys. Rev. Lett. 93(230501), 1–4 (2004)

    Google Scholar 

  17. Li, M., Fei, S.M., Li-Jost, X.Q., Fan, H.: Genuine multipartite entanglement detection and lower bound of multipartite concurrence. Phys. Rev. A 92(062338), 1–6 (2015)

    Google Scholar 

Download references

Acknowledgements

This work is supported by NSFC under numbers 11675113 and 11605083.

Author information

Authors and Affiliations

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

    Xue-Na Zhu

  2. College of the Science, China University of Petroleum, Qingdao, 266580, China

    Ming Li

  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. Ming Li
    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.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhu, XN., Li, M. & Fei, SM. A lower bound of concurrence for multipartite quantum systems. Quantum Inf Process 17, 30 (2018). https://doi.org/10.1007/s11128-017-1801-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-017-1801-x

Keywords

Search

Navigation