Weak measurement criteria for the past of a quantum particle

TL;DR

This paper critiques Vaidman's weak value criterion for determining the past of a quantum particle, showing its limitations in certain setups and proposing an alternative weak mean value criterion.

Contribution

It identifies the discontinuity issue in weak values in nested interferometers and introduces a more reliable weak mean value criterion for quantum particle history.

Findings

Weak values can be discontinuous and unreliable in certain quantum setups.

The proposed weak mean value criterion avoids the discontinuity problem.

The new criterion leads to different conclusions about photon paths in interferometers.

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.