Skip to main content
SpringerLink
Log in

Trade-Off Relations of CHSH Violations Based on Norms of Bloch Vectors

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

Abstract

By considering the norms of Bloch vectors, we present an improved trade-off relation of CHSH violations of pairwise qubits systems for any multi-qubit system, which leads to restrictions on the distribution of non-locality among the pairwise qubits systems. Detailed examples are computed to show that our result improves the trade-off relation in Qin et al. (Phys. Rev. A 92, 062339 2015). Our bounds are given by the norms of the Bloch vectors. Thus the bounds give experimentally feasible way in describing trade-off relation of maximal violations of CHSH inequalities for any multipartite-qubit state.

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. Bell, J.S.: On the Einstein-Poldolsky-Rosen Paradox. Physics 1, 159 (1964)

    Article  Google Scholar 

  2. Brukner, C., Zukowski, M., Zeilinger, A.: Quantum communication complexity protocol with two entangled qutrits. Phys. Rev. Lett 89, 197901 (2002)

    Article  ADS  Google Scholar 

  3. Scarani, V., Gisin, N.: Quantum communication between N Partners and Bell’s Inequalities. Phys. Rev. Lett. 87, 117901 (2001)

    Article  ADS  Google Scholar 

  4. Acin, A., Gisin, N., Scarani, V.: Security bounds in quantum cryptography using d-level systems. Quantum Inf. Comput 3, 563 (2003)

    MathSciNet  MATH  Google Scholar 

  5. Gisin, N.: Bell’s inequality holds for all non-product states. Phys. Rev. A 154, 201 (1991)

    Google Scholar 

  6. Gisin, N., Peres, A.: Maximal violation of Bell’s inequality for arbitrarily large spin. Phys. Lett. A 162, 15 (1992)

    Article  ADS  MathSciNet  Google Scholar 

  7. Popescu, S., Rohrlich, D.: Generic quantum nonlocality. Phys. Lett. A 166, 293 (1992)

    Article  ADS  MathSciNet  Google Scholar 

  8. Chen, J.L., Wu, C.F., Kwek, L.C., Oh, C.H.: Gisin’s theorem for three qubits. Phys. Rev. Lett 93, 140407 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  9. Li, M., Fei, S.M.: Gisin’s theorem for arbitrary dimensional multipartite states. Phys. Rev. Lett 104, 240502 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  10. Yu, S.X., Chen, Q., Zhang, C.J., Lai, C.H., Oh, C.H.: All entangled pure states violate a single Bell’s inequality. Phys. Rev. Lett 109, 120402 (2012)

    Article  ADS  Google Scholar 

  11. Koashi, M., Winter, A.: All entangled pure states violate a single Bell’s inequality. Phys. Rev. A 69, 022309 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  12. 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 

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

    Article  ADS  Google Scholar 

  14. de Oliveira, T.R., Cornelio, M.F., Fanchini, F.F.: Monogamy of entanglement of formation. Phys. Rev. A 89, 034303 (2014)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  16. Qin, H.H., Fei, S.M., Li-Jost, X.: Trade-off relations of Bell violations among pairwise qubit systems. Phys. Rev. A 92, 062339 (2015)

    Article  ADS  Google Scholar 

  17. Cheng, S.M., Hall, M.J.W.: Anisotropic invariance and the distribution of quantum correlations. Phys. Rev. Lett. 118, 010401 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  18. 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 

  19. Clauser, J.F., Horne, M.A., Shimony, A., Holt, R.A.: Proposed experiment to test local hidden-variable theories. Phys. Rev. Lett 23, 880 (1969)

    Article  ADS  MATH  Google Scholar 

  20. Bloch, F.: Nuclear induction. Phys. Rev 70, 460 (1946)

    Article  ADS  Google Scholar 

  21. Horodecki, M., Horodecki, P., Horodecki, R.: Two-spin-12 mixtures and Bell’s inequalities. Phys. Lett. A 210, 223 (1996)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  22. Hassan, A.S.M., Joag, P.S.: Geometric measure for entanglement in N-qudit pure states. Phys. Rev. A 80, 042302 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  23. Vértesi, T.: More efficient Bell inequalities for Werner states. Phys. Rev. A 78, 032112 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  24. Li, M., Zhang, T.G., Hua, B., Fei, S.M., Li-Jost, X.Q.: Quantum nonlocality of arbitrary dimensional bipartite states. Sci. Rep., 513358 (2015)

Download references

Acknowledgments

This work is supported by the NSFC No. 11775306, 11701568; the Fundamental Research Funds for the Central Universities Grants No. 17CX02033A and 18CX02023A; the Shandong Provincial Natural Science Foundation No. ZR2016AQ06, ZR2016AM23, ZR2017BA019.

Author information

Authors and Affiliations

  1. College of the Science, China University of Petroleum, 266580, Qingdao, People’s Republic of China

    Jing Wang, Zong Wang, Jiahuan Qiao, Ming Li & Shuqian Shen

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

    Ming Li

Authors
  1. Jing Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zong Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jiahuan Qiao
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ming Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Shuqian Shen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ming Li.

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

Wang, J., Wang, Z., Qiao, J. et al. Trade-Off Relations of CHSH Violations Based on Norms of Bloch Vectors. Int J Theor Phys 58, 1667–1675 (2019). https://doi.org/10.1007/s10773-019-04064-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-019-04064-0

Keywords

Search

Navigation