  We perform several numerical studies for our recently published adaptive
compressive tomography scheme [D. Ahn et al. Phys. Rev. Lett. 122, 100404
(2019)], which significantly reduces the number of measurement settings to
unambiguously reconstruct any rank-deficient state without any a priori
knowledge besides its dimension. We show that both entangled and product bases
chosen by our adaptive scheme perform comparably well with recently-known
compressed-sensing element-probing measurements, and also beat random
measurement bases for low-rank quantum states. We also numerically conjecture
asymptotic scaling behaviors for this number as a function of the state rank
for our adaptive schemes. These scaling formulas appear to be independent of
the Hilbert space dimension. As a natural development, we establish a faster
hybrid compressive scheme that first chooses random bases, and later adaptive
bases as the scheme progresses. As an epilogue, we reiterate important elements
of informational completeness for our adaptive scheme.
