The measured truth tables of retrieving the King’s choice of measurement. The empty histograms represent the theoretical probabilities while the color-filled histograms represent the experimentally measured probabilities, from which we can obtain the average reliability up to 0.813. According to the histograms beyond the threshold line (at probability 0.25 in the case of uniform distribution), Alice can retrodict the King’s choice of nonselective measurement in MUBs (indicated by on the center of each subgraphs) referring to Table 1. (a) When the initial state is . (b) When the initial state is . The error bars are calculated with Poisson statistics of the detection process taken into account.