  Probing ground-state quantum geometry and topology through optical response
is not only of fundamental interest, but it can also offer several practical
advantages. Here, using first-principles calculations on antiferromagnetic
topological insulator MnBi$_2$Te$_4$ thin films, we demonstrate how the
generalized optical weight arising from the absorptive part of the optical
conductivity can be used to probe the ground state quantum geometry and
topology. We show that three septuple layers MnBi$_2$Te$_4$ exhibit an enhanced
almost perfect magnetic circular dichroism for a narrow photon energy window in
the infrared region. We calculate the quantum weight in a few septuple layers
MnBi$_2$Te$_4$ and show that it far exceeds the lower bound provided by the
Chern number. Our results suggest that the well-known optical methods are
powerful tools for probing the ground state quantum geometry and topology.
