Quantumness of the anomalous weak measurement value

In Y. Aharonov et al. [Phys. Rev. Lett. 60, 1351 (1988)], it was shown that, in some weak measurements with postselection schemes, it is possible to obtain inferred mean values outside the range of the eigenvalues of the measured observable. In our work, we are going to show that this effect can be associated with the presence of an asymptotically vanishing but nonzero amount of system-detector quantum correlations. These correlations are also related to the presence of a finite (nonzero) amount of coherence of the initial states in the basis of the measured observable.