Weak measurements measure probability amplitudes (and very little else)

Abstract

Conventional quantum mechanics describes a pre- and post-selected system in terms of virtual (Feynman) paths via which the final state can be reached. In the absence of probabilities, a weak measurement (WM) determines the probability amplitudes for the paths involved. The weak values (VW) can be identified with these amplitudes, or their linear combinations. This allows us to explain the "unusual" properties of the VW, and avoid the "paradoxes" often associated with the WM.