Comment on “Null weak values and the past of a quantum particle”

In a recent paper [Phys. Rev. A 95, 032110 (2017)], Duprey and Matzkin investigated the meaning of vanishing weak values and their role in the retrodiction of the past of a preselected and postselected quantum system in the presence of interference. Here we argue that any proposition regarding the weak values should be understood as a statement about the probability amplitudes. With this in mind, we revisit some of the conclusions reached in Duprey and Matzkin's work.

Figure 1

(a) Three virtual paths with relative amplitudes $A_i, i=1,2,3$ (we omit the superscript $F\leftarrow I$) connect the initial and the final states of a particle. For $A_1=-A_2\ne 0$ and $A_3\ne 0$, a weak meter would give nonzero readings in the paths 1 and 2, but not in their superposition. (b) Same system but with paths 1 and 2 merged before and after the inner loop. The weak meter would give nonzero readings at $E$ and $E^{\prime }$, but not at $O$ and $O^{\prime }$, creating an impression that the particle was in the loop yet never entered or exited it.