Optimal error regions for quantum state estimation

Understand

Rather than point estimators, states of a quantum system that represent one's best guess for the given data, we consider optimal regions of estimators.

• As the natural counterpart of the popular maximum-likelihood point estimator, we introduce the maximum-likelihood region---the region of largest likelihood among all regions of the same size.
• Here, the size of a region is its prior probability.
• Another concept is the smallest credible region---the smallest region with pre-chosen posterior probability.