Operational formulation of weak values without probe systems

TL;DR

This paper presents a new operational formulation of weak values that directly relates to the system without needing a probe, clarifying their meaning and simplifying measurement procedures.

Contribution

It introduces a probe-free formulation of weak values based on sensitivity of post-selection amplitude, providing clearer interpretation and easier experimental implementation.

Findings

Weak values can be formulated as sensitivity of post-selection probability.

The new formulation removes the need for probe systems in measurements.

This approach simplifies weak-value measurement experiments.

Abstract

Weak values are the fundamental values for observables in a pre- and post-selected system. Weak values are typically measured by weak measurement, in which weak values appear in the change of not the pre- and post-selected system but the probe system. This indirect characteristic of weak measurement obscures the meaning of weak values for the pre- and post-selected system, in contrast to conventional physical quantities, which have a clear operational meaning. In this study, we operationally formulate weak values as the sensitivity of post-selection probability amplitude to small transformation in a pre- and post-selected system. This formulation of weak values, which is free from the concept of probe shift assumed in weak measurement, gives a direct interpretation of strange weak values for the pre- and post-selected system. We further explain that this formulation can simplify weak-value measurement experiments because no probe system is required.