  Quantised random embeddings are an efficient dimensionality reduction
technique which preserves the distances of low-complexity signals up to some
controllable additive and multiplicative distortions. In this work, we instead
focus on verifying when this technique preserves the separability of two
disjoint closed convex sets, i.e., in a quantised view of the "rare eclipse
problem" introduced by Bandeira et al. in 2014. This separability would ensure
exact classification of signals in such sets from the signatures output by this
non-linear dimensionality reduction. We here present a result relating the
embedding's dimension, its quantiser resolution and the sets' separation, as
well as some numerically testable conditions to illustrate it. Experimental
evidence is then provided in the special case of two $\ell_2$-balls, tracing
the phase transition curves that ensure these sets' separability in the
embedded domain.
