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  "path": "/abs/2605.15150v1",
  "publishedAt": "2026-05-15T00:00:00.000Z",
  "site": "https://arxiv.org",
  "tags": [
    "Yuzhen Zhang",
    "Isaac H. Kim",
    "Yimu Bao",
    "Sagar Vijay"
  ],
  "textContent": "**Authors:** Yuzhen Zhang, Isaac H. Kim, Yimu Bao, Sagar Vijay\n\nWe 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.",
  "title": "Extensive long-range magic in non-Abelian topological orders"
}