Quantum Tomography and Entanglement in Semi-Leptonic $h\to VV^*$ Decays at Higher Orders

Angular correlations in Higgs decays to electroweak gauge bosons, $h \to ZZ^*, WW^*$, provide a powerful probe of both new physics effects and quantum information observables. We present a systematic study of semi-leptonic decays $h \to V V^* \to \ell^+\ell^- q\bar{q}$ and $\ell^\pm \nu_\ell q\bar{q}'$, including finite final state fermion masses, NLO QCD, and NLO electroweak corrections. We show that finite final state quark masses can induce effects that go beyond the two-qutrit description in more inclusive regimes, while remaining controllable with suitable kinematic selections. QCD corrections lead to modest percent-level shifts, whereas electroweak corrections can significantly modify the angular structure, particularly in the $h\to ZZ^*$ channels. We assess the impact of these effects on the reconstructed density matrix and entanglement measures, finding that, while they modify the angular observables, semi-leptonic channels retain an effective two-qutrit description.