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.
Similar content being viewed by others
Notes
For discrete spectrum observables, the integral symbol is replaced by a discrete sum over the corresponding λα and λβ.
References
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)
Aspect, A., et al.: Experimental test of Bell's inequalities using time-varying analyzers. Phys. Rev. Lett. 49(25), 1804–1807 (1982)
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)
Lee, S.-W., Jeong, H., Jaksch, D.: Phys. Rev. A 80, 022104 (2009)
Wenger, J., Hafezi, M., Grosshans, F., Tualle-Brouri, R., Grangier, P.: Phys. Rev. A 67, 012105 (2003)
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)
Gleason, A.: Measures on the Closed Subspaces of a Hilbert Space. J. Math. Mech. 6, 885–893 (1957)
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)
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)
Uzan, P.: Deciding the Mind–body problem experimentally. Axiomathes 27(4), 333–354 (2017)
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10701-020-00342-8