Bell-like States in Classical Optics: A Process-Theoretic and Sheaf-Theoretic (Categorical) Clarification

• URL: http://arxiv.org/abs/2602.14508v1
• Date: Mon, 16 Feb 2026 06:40:05 GMT
• Title: Bell-like States in Classical Optics: A Process-Theoretic and Sheaf-Theoretic (Categorical) Clarification
• Abstract summary: Classical polarization optics is naturally described by a two-dimensional complex Hilbert space (Jones) vectors.<n>For statistical (stochastic) optical fields, suitably prepared two-beam polarization states can exhibit contextuality correlations of quantum strength.<n>The same platform offers a tunable, low-cost testbed for stress-testing Bell/CHSH and contextuality witnesses under realistic imperfections.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Classical polarization optics is naturally described by a two-dimensional complex Hilbert space (Jones vectors), so the tensor-product kinematics underlying bipartite nonseparability is already available classically. For statistical (stochastic) optical fields, and under an operational stance where outcomes are not assumed pre-assigned prior to detection, suitably prepared two-beam polarization states can exhibit Bell--CHSH correlations of quantum strength. The same platform offers a tunable, low-cost testbed for stress-testing Bell/CHSH and contextuality witnesses under realistic imperfections (noise, coarse binning, selective sampling). We also outline an alternative preparation based on external conical refraction (ECR), where engineered intersecting conical-refraction rings mimic the intersecting emission cones of SPDC. We give a self-contained categorical formulation: the preparation-and-conditioning pipeline (Hadamard-like splitting, CNOT-like coupling, and routing/conditioning that removes unwanted contributions) is treated as a single morphism in an operational process theory (e.g. $\mathbf{CPM}(\mathbf{FHilb})$). From it we functorially extract an empirical model, i.e. a compatible family of context-indexed probability distributions. The Abramsky--Brandenburger sheaf criterion then applies: noncontextuality is the existence of a global section, and CHSH violation is a precise failure-to-glue. This separates kinematic nonseparability from operational contextuality and clarifies why neither, by itself, entails nonlocal causation; contextuality can arise in a classically implementable stochastic-optics regime.

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