What is a quantum-mechanical 'weak value' the value of?

TL;DR

This paper critically examines the concept of 'weak values' in quantum mechanics, arguing that interpreting them as real properties of a system is unsupported by axioms and leads to unreasonable conclusions.

Contribution

It challenges the interpretation of weak values as genuine properties, providing a theoretical critique based on quantum axioms.

Findings

Weak values are not supported as real properties by quantum axioms

Interpreting weak values as system properties leads to unreasonable results

The paper questions the use of weak values in resolving quantum paradoxes

Abstract

A so called 'weak value' of an observable in quantum mechanics (QM) may be obtained in a weak measurement + post-selection procedure on the QM system under study. Applied to number operators, it has been invoked in revisiting some QM paradoxes (e.g., the so called Three Box paradox and Hardy s paradox). This requires the weak value to be interpreted as a bona fide property of the system considered, a par with entities like operator mean values and eigenvalues. I question such an interpretation; it has no support in the basic axioms of quantum mechanics and it leads to unreasonable results in concrete situations.