  We propose an estimation method for quantum measurement tomography (QMT)
based on semidefinite programming (SDP), and discuss how it may be employed to
detect experimental imperfections, such as shot noise and/or faulty preparation
of the input states on near-term quantum computers. Moreover, if the positive
operator-valued measure (POVM) we aim to characterize is informationally
complete, we put forward a method for self-consistent tomography, i.e., for
recovering a set of input states and POVM effects that is consistent with the
experimental outcomes and does not assume any a priori knowledge about the
input states of the tomography. Contrary to many methods that have been
discussed in the literature, our approach does not rely on additional
assumptions such as low noise or the existence of a reliable subset of input
states.
