# Identifying weak values with intrinsic dynamical properties in Modal theories

## TL;DR

This paper demonstrates that weak values in quantum mechanics can be understood as intrinsic dynamical properties within Modal theories, providing a new perspective on quantum properties independent of measurement context.

## Contribution

It establishes a link between weak values and intrinsic properties in Modal theories, expanding the understanding of quantum system dynamics beyond orthodox interpretations.

## Key findings

- Weak values correspond to intrinsic properties in Modal theories.
- Intrinsic properties like dwell time and work distribution are physically meaningful.
- Weak measurements can reveal unperturbed quantum dynamics.

## Abstract

The so-called eigenvalue-eigenstate link states that no property can be associated to a quantum system unless it is in an eigenstate of the corresponding operator. This precludes the assignation of properties to unmeasured quantum systems in general. This arbitrary limitation of Orthodox quantum mechanics generates many puzzling situations such as for example the impossibility to uniquely define a work distribution, an essential building block of quantum thermodynamics. Alternatively, Modal theories (e.g., Bohmian mechanics) provide an ontology that always allows to define intrinsic properties, i.e., properties of quantum systems that are detached from any possible measuring context. We prove here that Aharonov, Albert and Vaidman's notion of weak value can always be identified with an intrinsic dynamical property of a quantum system defined in a certain Modal theory. Furthermore, the fact that weak values are experimentally accessible (as an ensemble average of weak measurements which are post-selected by a strong measurement) strengthens the idea that understanding the intrinsic (unperturbed) dynamics of quantum systems is possible and useful in a given Modal theory. As examples of the physical soundness of these intrinsic properties, we discuss three intrinsic Bohmian properties, viz., the dwell time, the work distribution and the quantum noise at high frequencies.