statistics*]{}) of the light, for instance, the presence of Shot noise in the case of coherent beams, WVA does not offer any advantage regarding any decrease of the minimum probability of error achievable. This is shown by making use of the trace distance between quantum states or the Cramér-Rao inequality, which set sensitivity bounds that are independent of any particular post-selection. However, notice that this implicitly assume that full information about the quantum states used can be made available, and detectors are ideal, so they can detect any change of the variable of interest, as small as it might be, provided there is enough signal power.

Nevertheless, these assumptions are in many situations of interest far from true. These limitations, sometimes refereed as [*technical noise*]{}, even though not fundamental (one can always imagine using a better detector or a different detection scheme) are nonetheless important, since they limit the accuracy of specific detection systems at hand. In these scenarios, the importance of weak value amplification is that by decreasing the mode overlap associated with the states to be measured and possibly increasing the intensity of the signal, the weak value amplification scheme allows, in principle, to distinguish them with lower 