Bell Inequalities and Quantum Correlations in $H \rightarrow ZZ \rightarrow 2e\,2\mu$

We investigate quantum correlations in Higgs-boson decays $\bigl(H \rightarrow ZZ^* \rightarrow 2e\,2\mu\bigr)$ using CMS open data at $\sqrt{s}$ = 8 TeV, incorporating realistic detector effects. By reconstructing the polarization density matrix of the two-boson system and evaluating the Collins-Gisin-Linden-Massar-Popescu (CGLMP) Bell operator $I_3$, we quantify entanglement in the $ZZ$ state. Our analysis yields an $I_3$ value of $2.152 \pm 0.003$ for signal events $\bigl(H \rightarrow ZZ^*\bigr)$, indicating the presence of quantum entanglement. The non-resonant continuum background events $\bigl(pp \rightarrow ZZ\bigr)$ yield $I_3 = 1.158 \pm 0.012$, suggesting the absence of quantum correlations. These results demonstrate the feasibility of testing fundamental quantum mechanics at high energy colliders.