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On the relevance of Bell’s probabilistic model for spin correlations

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Abstract

In a recent article, Cetto et al. (Found Phys 50:27–39, 2020) present an elegant formalism analyzing the probabilistic properties of the quantum singlet state correlations. From their study, they conclude the quantum formalism entails a partitioning of the probability space which is supposed to be absent in Bell’s hidden variables probabilistic model. We formally prove that this is not the case and that Bell’s probabilistic model does indeed possesses the characteristic that is supposed to be missing. Therefore, contrary to their claim, their observation does not put into question the applicability of Bell-type inequalities to the bipartite singlet state.

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Notes

  1. We do not include \(\alpha _i,\beta _j\) as explicit arguments in \(\mathbf {\Lambda }_k({\mathbf {a}},{\mathbf {b}})\) because according to (7) the index k already determines them.

  2. The expression \(A_k=\alpha _i\beta _j\) should not be considered a functional factorization since \(\alpha _i\) and \(\beta _j\) represent constants used to classify the different eigenvalues according to the enumeration scheme (7).

  3. CL is known in the literature with different names: no-conspiracy, freedom, measurement independence, or statistical independence.

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  1. Facultad de Ciencias Exactas y Naturales, Ruta Mcal. J. F. Estigarribia, Km 11 Campus de la UNA, San Lorenzo, Paraguay

    Justo Pastor Lambare

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  1. Justo Pastor Lambare
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Lambare, J.P. On the relevance of Bell’s probabilistic model for spin correlations. Quantum Stud.: Math. Found. 9, 211–217 (2022). https://doi.org/10.1007/s40509-021-00265-7

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