Skip to main content
SpringerLink
Log in

The CHSH Test Can be Used for All Quantum-Describable Systems

  • Published:
Foundations of Physics Aims and scope Submit manuscript

Abstract

This paper shows that the Clauser–Horne–Shimony–Holt test of locality of correlations which was originally designed to be used with binary observables can actually be used for any couples of quantum-like bounded continuous observables, and then for any experimental situation describable within the mathematical framework of quantum theory.

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

Similar content being viewed by others

Notes

  1. For discrete spectrum observables, the integral symbol is replaced by a discrete sum over the corresponding λα and λβ.

References

  1. 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  Google Scholar 

  2. Aspect, A., et al.: Experimental test of Bell's inequalities using time-varying analyzers. Phys. Rev. Lett. 49(25), 1804–1807 (1982)

    Article  ADS  MathSciNet  Google Scholar 

  3. Tittel, W., Brendel, J., Gisin, B., Herzog, T., Zbinden, H., Gisin, N.: Experimental demonstration of quantum-correlations over more than 10 kilometers. Phys. Rev. A. 57(5), 3229–3232 (1998)

    Article  ADS  Google Scholar 

  4. Lee, S.-W., Jeong, H., Jaksch, D.: Phys. Rev. A 80, 022104 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  5. Wenger, J., Hafezi, M., Grosshans, F., Tualle-Brouri, R., Grangier, P.: Phys. Rev. A 67, 012105 (2003)

    Article  ADS  Google Scholar 

  6. A. Ketterer, A. Keller, T. Coudreau and P. Milman. Testing the Clauser-Horne-Shimony-Holt inequality using observables with arbitrary spectrum, Phy Rev. A 91(1) (2005)

  7. Gleason, A.: Measures on the Closed Subspaces of a Hilbert Space. J. Math. Mech. 6, 885–893 (1957)

    MathSciNet  MATH  Google Scholar 

  8. Plancherel, M.: Contribution à l’étude de la representation d’une fonction arbitraire par les integrales définies. Rendiconti del Circol Matematico di Palermo 30, 298–335 (1910)

    MATH  Google Scholar 

  9. Lamata, L., Léon, J.: Dealing with entanglement of continuous variables: Schmidt decomposition with discrete sets of orthogonal functions. J. Opt. B Quantum Semiclass. Opt. 7(2005), 224–229 (2005)

    Article  ADS  Google Scholar 

  10. Uzan, P.: Deciding the Mind–body problem experimentally. Axiomathes 27(4), 333–354 (2017)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratory SPHERE, Philosophy of Science, University Paris-Diderot, Building Condorcet, Case 7093, 5 rue Thomas Mann, 75205, Paris Cedex 13, France

    Pierre Uzan

Authors
  1. Pierre Uzan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Pierre Uzan.

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

Uzan, P. The CHSH Test Can be Used for All Quantum-Describable Systems. Found Phys 50, 708–714 (2020). https://doi.org/10.1007/s10701-020-00342-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10701-020-00342-8

Keywords

Search

Navigation