We provide a one-to-one map between the spin correlations and certain three-dimensional shapes, analogous to the map between single spins and Bloch vectors, and demonstrate its utility. Much as one can reason geometrically about dynamics using a Bloch vector---e.g., a magnetic field causes it to precess and dissipation causes it to shrink---one can reason similarly about the shapes we use to visualize correlations. This visualization demonstrates its usefulness by unveiling the hidden structure in the correlations. For example, seemingly complex correlation dynamics can be described as simple motions of the shapes. We demonstrate the simplicity of the dynamics, which is obscured in conventional analyses, by analyzing several physical systems of relevance to cold atoms.
AbstractWe present a geometric representation of bipartite quantum correlations based onglobal spinor structure rather than probabilistic hidden variables. The constructionreproduces the singlet correlation and provides an explicit mapping between mea-surement interaction and observed outcomes. The framework does not modify theempirical predictions of quantum mechanics, but supplies a non-factorisable mathe-matical representation in which outcomes arise through structural compatibility ratherthan sampling over counterfactual assignments. The analysis clarifies why Bell–CHSHfactorisations cannot be constructed within this representation and identifies the ob-struction as structural. The work addresses the representation of measurement andcorrelation structure within quantum theory.
We introduce the technique of entangled-beam reflectometry for extracting spatially correlated (magnetic or nonmagnetic) information from material surfaces or thin films. Our amplitude- and phase-sensitive technique exploits the coherent nature of an incoming entangled probe beam, of matter or light waves, undergoing reflection from the surface. Such reflection encodes the surface spatial structure into the probe's geometric and phase-derived Goos-Hänchen shifts, which can then be measured to unveil the structure. We investigate the way these shifts depend on the wave packet widths, and illustrate our technique in the case of in-plane periodic (non)magnetic structures by utilizing spin-path mode-entangled neutron beams.
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
ν=π/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.