Weak values could reveal the hidden effects of quantum interactions

Due to the reduced probability of successful post-selection, the weak-value amplification seems to be unavailable for the parameter-estimation. Here, we show theoretically that, some effects due to the weak interactions present only in the properly post-selected sub-ensemble, however are canceled by themselves in the total ensemble. From this point of view, the post-selection induced weak value could be one of the feasible methods for measuring the weak interaction, since the standard measurement does not work. Additionally, we employ the system of trapped ions to simulate the weak measurement and calculate relevant results without the frequently-used weak interaction approximation.