Quantum computers gain their advantage from magic — a resource property of quantum states that measures how far they are from the stabilizer states that can be efficiently simulated classically. A state with no magic is a stabilizer state: it can be prepared by Clifford gates alone, and any computation it participates in can be efficiently replicated on a classical computer. Magic is what makes quantum computation hard to simulate.
Noise destroys magic. Environmental decoherence pushes quantum states toward the stabilizer polytope — the convex hull of all stabilizer states in the Bloch representation. The question is: at what noise level does a state lose its computational advantage?
Zurel and Davis (arXiv 2602.22336, February 2026) introduce a basis-independent framework for answering this question. Most measures of magic depend on the choice of basis — rotating the coordinate system can change whether a state appears magical or not. The authors characterize absolutely stabilizer states: states that are stabilizer states in every basis simultaneously. These are states so deeply unmagical that no rotation can rescue them.
For a single qubit, the absolutely stabilizer states form a ball inscribed in the stabilizer octahedron — the largest sphere that fits inside the polytope. Any state inside this ball is classically simulable regardless of how you orient your measurement axes. Any state outside it has some basis in which it has magic.
But the geometric picture reveals a subtlety. Absolutely Wigner-positive states — states whose Wigner function remains non-negative in every basis — are a different set. Some absolutely Wigner-positive states are not absolutely stabilizer states. These states have non-negative Wigner functions everywhere (a classical-seeming property) but are not stabilizer states (they sit outside the stabilizer polytope in some basis). They have magic that cannot be extracted — bound magic, in analogy with bound entanglement.
Bound magic represents quantum computational resource that exists but cannot be utilized. The state is non-classical by one measure and classical by another. Noise has partially destroyed the advantage but left behind a ghost of it — detectable but inoperative.
The minimum purity for a state to retain any magic, computed from the inscribed ball radius, sets a noise threshold: above this noise level, no amount of basis rotation can reveal useful non-classicality. Below it, some orientation exists where the state has magic. The threshold is geometric — it depends on the shape of the stabilizer polytope, not on any particular magic monotone.