Tripartite entanglement in $H \to ZZ,WW$ decays

The decays of the Higgs boson produce a state in which the spins of the decay products and the orbital angular momentum ($L$) are highly entangled. We obtain the tripartite density operator, as well as reduced operators, for the decay into two weak bosons. For $H \to ZZ$ in the four-lepton final state we also estimate the statistical sensitivity at the Large Hadron Collider and future upgrades, using a binned method to reconstruct the density operators from distributions. With the expected Run 3 data, establishing genuine tripartite entanglement would be possible beyond the $5\sigma$ level. The violation of Bell inequalities involving the spins of the two weak bosons could also be established beyond the $5\sigma$ level.