  Because of the constraint that the estimators be bona fide physical states,
any quantum state tomography scheme - including the widely used maximum
likelihood estimation - yields estimators that may have a bias, although they
are consistent estimators. Schwemmer et al. (arXiv:1310.8465 [quant-ph])
illustrate this by observing a systematic underestimation of the fidelity and
an overestimation of entanglement in estimators obtained from simulated data.
Further, these authors argue that the simple method of linear inversion
overcomes this (perceived) problem of bias, and there is the suggestion to
abandon time-tested estimation procedures in favor of linear inversion. Here,
we discuss the pros and cons of using biased and unbiased estimators for
quantum state tomography. We conclude that the little occasional benefit from
the unbiased linear-inversion estimation does not justify the high price of
using unphysical estimators, which are typically the case in that scheme.
