Basis-independent stabilizerness and maximally noisy magic states

• URL: http://arxiv.org/abs/2602.22336v1
• Date: Wed, 25 Feb 2026 19:03:16 GMT
• Title: Basis-independent stabilizerness and maximally noisy magic states
• Authors: Michael Zurel, Jack Davis,
• Abstract summary: We show a characterization of absolutely stabilizer states for multiple qudits of all prime dimensions by introducing a polytope of their allowed spectra.<n>For odd-prime-dimensional qudits, we also give a complete characterization of absolutely Wigner-positive states.
• Score: 0.21485350418225238
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Absolutely stabilizer states are those that remain convex mixtures of stabilizer states after conjugation by any unitary. Here we give a characterization of such states for multiple qudits of all prime dimensions by introducing a polytope of their allowed spectra. We illustrate this through the examples of one qubit, two qubits, and one qutrit. In particular, the set of absolutely stabilizer states for a single qubit is a ball inscribed in the stabilizer octahedron, but for higher dimensions the geometry is more complicated. For odd-prime-dimensional qudits, we also give a complete characterization of absolutely Wigner-positive states, i.e., states whose Wigner function remains nonnegative after conjugation by any unitary. In so doing, we show there are absolutely Wigner-positive states that are not absolutely stabilizer, which can be seen as a unitarily-invariant version of bound magic. We then study the radii of the largest balls contained in the sets of absolutely stabilizer states and absolutely Wigner-positive states. These radii respectively tell us the lowest possible purity of nonstabilizer and Wigner-negative states. Conversely, we also find the radius of the smallest ball containing the set of absolutely Wigner-positive states, giving a tight purity-based necessary condition thereof.

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