How weak values illuminate the role of "hidden"-variables as predictive tools

TL;DR

This paper explores how weak values serve as predictive tools in quantum mechanics, highlighting their experimental determination, formal correlates, and ontological significance across different interpretations, with a case study on quantum thermalization.

Contribution

It introduces the role of weak values as predictive and characterizing tools in quantum systems, emphasizing their heuristic value in hidden-variable theories like Bohmian mechanics.

Findings

Weak values can predict quantum thermalization times.

Bohmian mechanics helps identify physically relevant weak values.

Standard expectation values are insensitive to thermalization onset.

Abstract

In this chapter we offer an introduction to weak values from a three-fold perspective: first, outlining the protocols that enable their experimental determination; next, deriving their correlates in the quantum formalism and, finally, discussing their ontological significance according to different quantum theories or interpretations. We argue that weak values have predictive power and provide novel ways to characterise quantum systems. We show that this holds true regardless of ongoing ontological disputes. And, still, we contend that certain "hidden" variables theories like Bohmian mechanics constitute very valuable heuristic tools for identifying informative weak values or functions thereof. To illustrate these points, we present a case study concerning quantum thermalization. We show that certain weak values, singled out by Bohmian mechanics as physically relevant, play a crucial role in elucidating the thermalization time of certain systems, whereas standard expectation values are "blind" to the onset of thermalization.