  In the context of quantum tomography, we recently introduced a quantity
called a partial determinant \cite{jackson2015detecting}. PDs (partial
determinants) are explicit functions of the collected data which are sensitive
to the presence of state-preparation-and-measurement (SPAM) correlations.
Importantly, this is done without any need to estimate state-preparation or
measurement parameters. In the present work, we wish to better explain our
theoretical perspective behind the PD. Further, we would like to demonstrate
that there is an overwhelming variety of applications and generalizations of
the PD. In particular we will construct methods for detecting SPAM correlations
in multiqudit systems. The relationship between the PDs of each method and the
correlations they are sensitive to is topological. We give a classification of
all such methods but focus on explicitly detailing only the most scalable
methods, $\mathcal{O}(d^4)$.
