Quantum tomography of $H\to ZZ,WW$ beyond leading order

We revisit quantum tomography of $H\to ZZ$ and $H\to WW$ in the presence of higher-order corrections. We verify that neither the use of an effective spin analysing power (only for $ZZ$) or a photon veto are sufficient to render the naively-constructed spin density operators physical. A subtraction of higher-order corrections is thus necessary to perform consistent quantum tomography. Such corrections are small when compared to expected experimental uncertainties with current data. As a by-product, we point out the striking possibility to observe parity-violating effects in $H\to WW$.