This analysis demonstrates Bell-inequality violation in Fibonacci anyon braiding, indicating topological non-separability in quantum systems.
We report the first complete numerical enumeration of Bell-inequality violation across all Fibonacci anyon braiding sequences of length L = 3–12 in two complementary encodings of six anyons. In the two-generator d1b encoding (native four-dimensional fusion space), the optimal sequence at L = 12 reaches |S| = 2.811 (99.4% of the Tsirelson bound). In the three-generator encoding (full five-dimensional fusion space), Tsirelson saturation occurs already at L = 8. Bell violation is generic: 64.6% of sequences violate CHSH under native 5D measurement, 91.8% under computational-subspace projection. Blocking the cross-bipartition generator σ₃ collapses concurrence to C = 0 exactly — topology acts as a gatekeeper. Sequential braiding produces ACF(1) = +0.34 at 10.85σ, a falsifiable prediction absent in standard quantum mechanics. v1.2: Abstract qualifier added; unused bibitems removed; 'determines' softened to 'governs'; ACF prediction phrasing aligned with TCH. v1.3: Non-separability framing footnote added in Abstract (after "Bell violation is generic"); clarifying sentence inserted in Conclusion before companion-paper reference; v1.3 Note added after . Clarifies that "Bell violation" refers to CHSH values on a Fibonacci fusion space that does not tensor-factorize, constituting a signature of topological non-separability rather than an EPR-type Bell violation. No numerical results or claims of v1.0/v1.1/v1.2 affected; framing language refined for consistency with the companion TCH theoretical framework paper (forthcoming v1.4).
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Berkay Yüksel Sayim (2026) studied this question.
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