Figure 4: Analysis of the interaction-free measurements.

(a) After the unbalanced homodyning, the counting statistics in the presence (orange bars) and absence (blue bars) of the Zeno suppression are very different and may be used to distinguish the ‘with object’ and ‘without object’ case. The error bars indicate the expected statistical noise for the finite set of measurements. (b) The counting statistics in the ‘with object’ case (orange circles) can be reproduced by a weighted sum (solid orange line) of Hermite polynomials (dashed lines) corresponding to the Fock states |n〉 with n=0, 1, 2, 3 and 4. (c) Based on a Maximum Likelihood analysis, we can determine the weights w_n of the individual Fock states. Most importantly, the vacuum contribution of 67(2)% shows that most measurements are indeed interaction-free. (d) Based on a given single measurement result (corresponding to the x-axis), the probabilities for the three possible cases are given: ‘with object’ (orange line), ‘without object’ (blue line) and the case where an interaction has occurred (grey line). These results were obtained from a Bayesian analysis with an uninformative prior. The lines’ thicknesses correspond to the uncertainties of these probabilities. The uncertainties in b, c and d are derived from the expected statistical uncertainties in a by a bootstrapping method³⁷.