Weak values and quantum properties

TL;DR

This paper explores the interpretation of weak values in quantum mechanics, proposing they represent a weaker form of property ascription than eigenvalues, thus offering a nuanced understanding of quantum properties.

Contribution

It clarifies the meaning of weak values within the property ascription framework, linking them to a partial description of quantum systems beyond traditional eigenvalue-based properties.

Findings

Weak values can be interpreted as a weaker form of property ascription.

Weak measurements are consistent with standard quantum formalism.

Weak values provide a partial description of quantum properties.

Abstract

We investigate in this work the meaning of weak values through the prism of property ascription in quantum systems. Indeed, the weak measurements framework contains only ingredients of the standard quantum formalism, and as such weak measurements are from a technical point of view uncontroversial. However attempting to describe properties of quantum systems through weak values -- the output of weak measurements -- goes beyond the usual interpretation of quantum mechanics, that relies on eigenvalues. We first recall the usual form of property ascription, based on the eigenstate-eigenvalue link and the existence of "elements of reality". We then describe against this backdrop the different meanings that have been given to weak values. We finally argue that weak values can be related to a specific form of property ascription, weaker than the eigenvalues case but still relevant to a partial description of a quantum system.