  There is an enormous amount of information that can be extracted from the
data of a quantum gas microscope that has yet to be fully explored. The quantum
gas microscope has been used to directly measure magnetic order, dynamic
correlations, Pauli blocking, and many other physical phenomena in several
recent groundbreaking experiments. However, the analysis of the data from a
quantum gas microscope can be pushed much further, and when used in conjunction
with theoretical constructs it is possible to measure virtually any observable
of interest in a wide range of systems. We focus on how to measure quantum
entanglement in large interacting quantum systems. In particular, we show that
quantum gas microscopes can be used to measure the entanglement of interacting
boson systems exactly, where previously it had been thought this was only
possible for non-interacting systems. We consider algorithms that can work for
large experimental data sets which are similar to theoretical variational Monte
Carlo techniques, and more data limited sets using properties of correlation
functions.
