Optimal Data Processing for Quantum Measurements

We consider the general measurement scenario in which the ensemble average of an operator is determined via suitable data processing of the outcomes of a quantum measurement described by a positive operator-valued measure. We determine the optimal processing that minimizes the statistical error of the estimation.

Figure 1

Example of optimized data-processing rule for the informationally complete POVM in Eq. (29). The plot shows the relative added noise in Eq. (27) for $X={\sigma }_z+x{\sigma }_x+y{\sigma }_y$ versus $x$ and $y$.