Optimization-Based Magic Measures Produce Energy-Independent Weak Mixing Angle Unlike SRE

The arXiv preprint demonstrates that maximal-magic states and derived physical quantities depend on the chosen magic monotone. Exact proofs establish distinct maximizers for each of the four measures examined. When applied to extracting the weak mixing angle, the stabilizer Rényi entropy and min-relative entropy produce differing energy dependence, whereas the two optimization-based measures remain constant.

This result arises because optimization-based monotones are non-analytic at certain state boundaries, creating flat regions where the weak mixing angle is pinned. The finding directly challenges the community’s default reliance on SRE for high-energy and nuclear applications. It shows that conclusions about fundamental parameters can shift with the resource measure selected.

Context from prior work on quantum resources indicates that similar measure dependence has already altered interpretations in magic-state distillation thresholds. Extending the comparison to three or more qubits and to lattice gauge theories would test whether the discrepancy persists at scales relevant to collider phenomenology.

Future experiments at facilities measuring precision electroweak observables could adopt multiple monotones in parallel analyses to quantify systematic uncertainty introduced by the choice of magic measure.