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.
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For discrete spectrum observables, the integral symbol is replaced by a discrete sum over the corresponding λα and λβ.
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)
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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
- CHSH test
- Quantum-like description