Null weak values and the past of a quantum particle

TL;DR

This paper investigates the meaning of vanishing weak values in quantum measurements, analyzing their implications for understanding a particle’s past and providing a new example of apparent discontinuous trajectories.

Contribution

It introduces a novel analysis of null weak values and their implications for quantum particle trajectories, contrasting with previous interpretations.

Findings

Vanishing weak values can indicate discontinuous particle trajectories.

A new non-optical example demonstrates apparent discontinuous paths.

Comparison with previous results clarifies the physical meaning of weak values.

Abstract

Non-destructive weak measurements (WM) made on a quantum particle allow to extract information as the particle evolves from a prepared state to a finally detected state. The physical meaning of this information has been open to debate, particularly in view of the apparent discontinuous trajectories of the particle recorded by WM. In this work we investigate the properties of vanishing weak values for projection operators as well as general observables. We then analyze the implications when inferring the past of a quantum particle. We provide a novel (non-optical) example for which apparent discontinuous trajectories are obtained by WM. Our approach is compared to previous results.