All standard scalar quantum-information measures—concurrence, negativity, entanglement entropy, the optimized Clauser-Horne-Shimony-Holt bound, and quantum Fisher information—are $CP$ blind in ideal $\mathrm{spin}\text{−}0\to f\overline{f}$ decays because the two-qubit spin state is maximally entangled for every $CP$ angle. We show that the stabilizer Rényi entropy, evaluated in the physical Pauli frame of spin analysis, escapes this blind spot: it admits an exact closed form, vanishing at $CP$-definite and Clifford phases and peaking at maximal non-Clifford mixing. Two experimentally accessible, nonstabilizerness-inspired $CP$ witnesses follow; the linear amplitude is 14.3 times more efficient than its quartic counterpart and reaches discovery-level sensitivity at the HL-LHC for $H\to {\tau }^{+}{\tau }^{-}$.

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• Quantum correlations, foundations & formalism