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arXiv · 2611.08586

Magic Is in the Eye of the Measure

Zhi-Heng Shen·Zhewei Yin·Hao-Lin Zhang
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Abstract

Magic, or nonstabilizerness, is the quantum resource behind universal quantum computation. Its applications in high-energy and nuclear physics rely almost exclusively on the stabilizer Rényi entropy (SRE), although magic has no unique measure. For two qubits, we compare the SRE with three measures defined through optimizations over stabilizer states: the min- and max-relative entropies of magic and the logarithmic free robustness. We determine the maximal-magic states of all four measures, with exact proofs, and find that they depend on the measure. In the determination of the weak mixing angle from minimal magic in Møller scattering, the min-relative entropy gives an energy-dependent value that differs from that of the SRE, whereas the max-relative entropy and the logarithmic free robustness give $\sin^2θ_W=1/4$ at all energies. We trace this difference to the non-analytic structure of the optimization-based measures. Physical conclusions drawn from extremizing magic can thus depend on the measure.

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Zhi-Heng Shen, Zhewei Yin, Hao-Lin Zhang. 2026-11-05. Magic Is in the Eye of the Measure. https://arxiv.org/abs/2611.08586

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