Published February 23, 2026
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Topology-Induced Gaussian Entanglement and Boundary Bell Nonlocality in Classical Field
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Topology-Induced Gaussian Entanglement and Boundary Bell Nonlocality
This research presents a rigorous classical-to-quantum bridge, demonstrating how quantum entanglement and Bell nonlocality emerge from the dynamics of a classical complex scalar field. We investigate commensurable topological vortex pairs, defined as stable, closed toroidal defects on a periodic three-torus, acting as fundamental particle analogues. A key finding is an exact analytical identity mapping the measured energy Hessian of these classical field configurations directly to quantum log-negativity, a measure of Gaussian entanglement. Numerical simulations at production resolution (N=288) robustly verify this quantum bridge. Our work reveals that the magnitude of inter-core entanglement is governed by a novel harmonic index, rather than solely by the greatest common divisor (gcd) of topological winding numbers, establishing commensurability as a channel-admissibility condition. This represents a significant departure from conventional understanding of topological interactions. Furthermore, we conduct comprehensive stress-tests for Bell nonlocality using the Banaszek-Wódkiewicz CHSH inequality on the derived Gaussian states. We observe robust Bell violation for several heteronuclear vortex pairs across wide separation ranges, confirming the presence of genuine quantum nonlocality originating from classical field geometry. Crucially, the study precisely identifies boundary regimes where states remain entangled but become Bell-local under strict numerical thresholds. This distinction between entanglement and Bell nonlocality, derived from a classical field framework, offers profound insights into the foundations of quantum mechanics. The methodology provides a unique, deterministic mechanism for quantum phenomena to arise from deeper classical field structures. This work offers a novel perspective on quantum correlations, with potential implications for fundamental physics, particle analogues, and quantum information science. It challenges existing paradigms by providing a classical, geometric underpinning for phenomena typically considered exclusively quantum. The rigorous numerical validation and theoretical coherence underscore the breakthrough nature of these findings. This research is poised to significantly impact our understanding of the classical-quantum interface.
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ENTANGLEMENT_AND_NONLOCALITY_IN_COMMENSURABLE_TOPOLOGICAL_VORTEX_PAIRS.pdf
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- Submitted
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2026-02-23