State and measurement tomography make assumptions about the experimental
states or measurements. These assumptions are often not justified because state
preparation and measurement errors are unavoidable in practice. Here we
describe how the Gram matrix associated with the states and measurement
operators can be estimated via semidefinite programming if the states and the
measurements are so called globally completable. This is for instance the case
if the unknown measurements are known to be projective and non-degenerate. The
computed Gram matrix determines the states, and the measurement operators
uniquely up to simultaneous rotations in the space of Hermitian matrices. We
prove the reliability of the proposed method in the limit of a large number of
independent measurement repetitions.Comment: We have completely rewritten the first version because new results
from arXiv:1209.6499 allowed to significantly clearify the first submission.
We have added some reference
