  This work analyzes correlations arising from quantum systems subject to
sequential projective measurements to certify that the system in question has a
quantum dimension greater than some $d$. We refine previous known methods and
show that dimension greater than two can be certified in scenarios which are
considerably simpler than the ones presented before and, for the first time in
this sequential projective scenario, we certify quantum systems with dimension
strictly greater than three. We also perform a systematic numerical analysis in
terms of robustness and conclude that performing random projective measurements
on random pure qutrit states allows a robust certification of quantum
dimensions with very high probability.
