  In quantum state tomography, the estimated frequencies do not correspond
directly to a physical quantum state, due to statistical fluctuations. Thus,
one resorts to point estimators that return the state that matches observations
the best, and a variety of estimators have been proposed -- linear inversion,
least squares, maximum likelihood (ML) -- each making different trade-offs. In
this short note, we investigate an alternative approach inspired by
device-independent quantum information protocols. We embed a tomographic
complete set of measurement operators within the framework of a Bell scenario,
and first regularize the estimated frequencies using a device-independent
maximum likelihood algorithm. We then run the standard maximum likelihood
algorithm to estimate the underlying quantum state. In this preliminary
investigation, we do not observe significant differences in the reconstructed
state when using the new algorithm.
