Contextual Values of Observables in Quantum Measurements

TL;DR

This paper introduces the concept of contextual values in quantum measurements, providing a unified framework that generalizes eigenvalues and clarifies the theoretical basis of quantum weak values, with implications for experiments and theory.

Contribution

It develops a general theoretical framework for contextual values, addressing controversies around quantum weak values and connecting to existing experimental and theoretical results.

Findings

Defines contextual values as a generalization of eigenvalues.

Shows convergence of conditioned averages to quantum weak values.

Provides examples linking theory to experiments.

Abstract

We introduce contextual values as a generalization of the eigenvalues of an observable that takes into account both the system observable and a general measurement procedure. This technique leads to a natural definition of a general conditioned average that converges uniquely to the quantum weak value in the minimal disturbance limit. As such, we address the controversy in the literature regarding the theoretical consistency of the quantum weak value by providing a more general theoretical framework and giving several examples of how that framework relates to existing experimental and theoretical results.