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arXiv · 2606.12045

A Geometric Family of Correlations Containing the Quantum Singlet

E. Aldo Arroyo
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Abstract

We introduce a geometrically constrained hidden-variable framework that generates a family of correlations parametrized by a boundary function, within which the quantum singlet correlation appears as a particular member. Exact expressions for the correlation function are derived. Several structural results are established, including admissibility conditions, symmetry properties, a universal stationary point of the associated CHSH function, and an exact relation between the CHSH value at $\nu=\pi/4$ and a geometric contrast measure defined on the underlying hidden-variable distributions. Rather than treating the quantum singlet correlation as an isolated target to be reproduced, the present framework places it within a broader geometric structure of correlations. These results suggest the existence of a nontrivial geometric structure underlying the family of correlations and motivate the search for a principle capable of selecting the quantum singlet solution from within that family.

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E. Aldo Arroyo. 2026-06-10. A Geometric Family of Correlations Containing the Quantum Singlet. https://arxiv.org/abs/2606.12045

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