  Higgs boson decays produce pairs of $W$ bosons in a maximally entangled
state, the spins of which can be expected to violate Bell inequalities. We show
that the spin density matrix of the $W^\pm$ pair may be reconstructed
experimentally from the directions of the charged lepton decay products, and
from it the expectation values of various Bell operators determined. Numerical
simulations of $H\rightarrow WW^*$ decays indicate that violation of a
generalised CHSH inequality is unlikely to be measurable, however the CGLMP
inequality is near-maximally violated. Experimental Bell tests could be
performed at a variety of colliders and in different production channels. If
reconstruction effects and backgrounds can be controlled then statistically
significant violations could be observable even with datasets comparable to
those already collected at the LHC.
