Weak measurement criteria for the past of a quantum particle

Abstract

Vaidman, Phys.Rev. A 87, 052104 (2013), has proposed a weak value criterion for the past of a quantum particle, and applied it to photons in a particular setup of nested Mach-Zehnder interferometers. From his analysis, he draws some astonishing conclusions regarding which arms of the setup the photons populate. I argue that the weak values Vaidman employs as weak tracers in his analysis cannot be used in this case and that, consequently, the conclusions he draws cannot be upheld. The reason is that weak values are defined as a limit which in this case turns out to be discontinuous. I propose instead a weak mean value criterion which avoids these shortcomings.