  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.
