Classical Field Approach to Quantum Weak Measurements

TL;DR

This paper extends the concept of weak measurements from quantum mechanics to quantum fields, showing they reveal an effective classical background field that encodes average field configurations and obeys equations of motion derived from an effective action.

Contribution

It introduces a generalized framework for weak measurements in quantum fields, linking weak values to classical background fields and their dynamics, which was not previously established.

Findings

Weak measurements probe an effective classical background field.

The classical field is a weak value of the quantum field operator.

Weak measurements perturb the effective action, affecting classical field dynamics.

Abstract

By generalizing the quantum weak measurement protocol to the case of quantum fields, we show that weak measurements probe an effective classical background field that describes the average field configuration in the spacetime region between pre- and post-selection boundary conditions. The classical field is itself a weak value of the corresponding quantum field operator and satisfies equations of motion that extremize an effective action. Weak measurements perturb this effective action, producing measurable changes to the classical field dynamics. As such, weakly measured effects always correspond to an effective classical field. This general result explains why these effects appear to be robust for pre- and post-selected ensembles, and why they can also be measured using classical field techniques that are not weak for individual excitations of the field.