  We investigate numerically several proxy measures for the number of states
contained within the holographic entropy cone, compared to the number contained
within the quantum entropy cone, for states with $3$ and $4$ parties. We find
an interesting tension: while measures focused on calculating the volume ratios
between the two cones indicate that the quantum cone is much larger than the
holographic one, measures based on the generation of random states and then
calculating the entropies thereof imply that almost all such randomly generated
states are also contained within the holographic entropy cone. Also
interestingly, the volume measures strongly indicate a difference in the number
of states within the quantum or stabiliser cones versus the number in the
holographic cone, which is not reproduced by the other classes of measures. We
comment on the difference between the two classes of measures, and why each may
be preferable.
