Error probability analysis in quantum tomography: a tool for evaluating experiments

Understand

We expand the scope of the statistical notion of error probability, i.e., how often large deviations are observed in an experiment, in order to make it directly applicable to quantum tomography.

• We verify that the error probability can decrease at most exponentially in the number of trials, derive the explicit rate that bounds this decrease, and show that a maximum likelihood estimator achieves this bound.
• We also show that the statistical notion of identifiability coincides with the tomographic notion of informational completeness.
• Our result implies that two quantum tomographic apparatuses that have the same risk function, (e.g.