Weak values of a quantum observable and the cross-Wigner distribution

TL;DR

This paper explores the weak values of quantum observables through the cross-Wigner distribution, linking quantum interference phenomena to time-frequency analysis concepts.

Contribution

It introduces a novel approach using the cross-Wigner transform to express weak values as complex probability distributions, connecting quantum mechanics with radar and time-frequency analysis.

Findings

Weak values are expressed via the cross-Wigner distribution.

The approach supports the idea that weak values result from interference of past and future wavefunctions.

The method bridges quantum measurement theory with time-frequency analysis techniques.

Abstract

We study the weak values of a quantum observable from the point of view of the Wigner formalism. The main actor is here the cross-Wigner transform of two functions, which is in disguise the cross-ambiguity function familiar from radar theory and time-frequency analysis. It allows us to express weak values using a complex probability distribution. We suggest that our approach seems to confirm that the weak value of an observable is, as conjectured by several authors, due to the interference of two wavefunctions, one coming from the past, and the other from the future.