<i>Colloquium</i>: Understanding quantum weak values: Basics and applications

TLDR

The quantum weak value has evolved from a theoretical curiosity to a practical laboratory tool, yet its interpretation remains historically confusing. This review offers a pragmatic introduction to weak values, explaining how to measure them experimentally and surveying their use in three distinct techniques. The authors illustrate three experimental uses of weak values—signal amplification, direct state and geometric phase measurement, and probing nonclassical features—using a single experimental configuration.

Abstract

Since its introduction 25 years ago, the quantum weak value has gradually transitioned from a theoretical curiosity to a practical laboratory tool. While its utility is apparent in the recent explosion of weak value experiments, its interpretation has historically been a subject of confusion. Here a pragmatic introduction to the weak value in terms of measurable quantities is presented, along with an explanation for how it can be determined in the laboratory. Further, its application to three distinct experimental techniques is reviewed. First, as a large interaction parameter it can amplify small signals above technical background noise. Second, as a measurable complex value it enables novel techniques for direct quantum state and geometric phase determination. Third, as a conditioned average of generalized observable eigenvalues it provides a measurable window into nonclassical features of quantum mechanics. In this selective review, a single experimental configuration to discuss and clarify each of these applications is used.