Experimentally efficient methods for estimating the performance of quantum measurements

Efficient methods for characterizing the performance of quantum measurements are important in the experimental quantum sciences. Ideally, one requires both a physically relevant distinguishability measure between measurement operations and a well-defined experimental procedure for estimating the distinguishability measure. Here, we propose the average measurement fidelity and error between quantum measurements as distinguishability measures. We present protocols for obtaining bounds on these quantities that are both estimable using experimentally accessible quantities and scalable in the size of the quantum system. We also explain why the bounds should be valid in large generality and illustrate the method via numerical examples.

Figure 1

Plot of exact average measurement fidelity $\overline{F_{\mathcal{E},\mathcal{M}}}$ [dashed (blue) curve] versus coherence strength $\left|\gamma \right|$ for three values of $u_0$: $0.99$ (top left), $0.995$ (bottom left), and $0.999$ (bottom right). The lower bound $lb$ for $\overline{F_{\mathcal{E},\mathcal{M}}}$ in each case is also given [horizontal (green) line]. The magnitude of the coherence was varied in each case up to its maximum value, $R_{\text{max}}$.