Extensive long-range magic in non-Abelian topological orders

• URL: http://arxiv.org/abs/2605.15150v1
• Date: Thu, 14 May 2026 17:50:20 GMT
• Title: Extensive long-range magic in non-Abelian topological orders
• Abstract summary: We show that low-energy states of non-Abelian topological orders possess extensive magic which is long-ranged.<n>We argue that any state obeying an entanglement area law and hosting excitations with nontrivial fusion spaces must exhibit extensive long-range magic.
• Score: 3.8943557849328023
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We show that the low-energy states of non-Abelian topological orders possess extensive magic which is long-ranged, and cannot be eliminated by a constant-depth local unitary circuit. This refines conventional notions of complexity beyond the linear circuit depth which is required to prepare any topological phase, and provides a new resource-theoretic characterization of topological orders. A central technical result is a no-go theorem establishing that stabilizer states--even up to constant-depth local unitarie--cannot approximate low-energy states of non-Abelian string-net models which satisfy the entanglement bootstrap axioms. Moreover, we show that stabilizer-realizable Abelian string-net phases have mutual braiding phases quantized by the on-site qudit dimension, and that any violation of this condition necessarily implies extensive long-range magic. Extending to higher spatial dimensions, we argue that any state obeying an entanglement area law and hosting excitations with nontrivial fusion spaces must exhibit extensive long-range magic. This applies, in particular, to ground-states and low-energy states of higher-dimensional quantum double models.

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