  Joint measurability of sharp quantum observables is determined pairwise, and
so can be captured in a graph. We prove the converse: any graph, whose vertices
represent sharp observables, and whose edges represent joint measurability, is
realised by quantum theory. This leads us to show that it is not always
possible to use Neumark dilation to turn unsharp observables into sharp ones
with the same joint measurability relations, highlighting a caveat in the
church of the larger Hilbert space".
