A detector-based measurement theory for quantum field theory

TL;DR

This paper develops a measurement theory for quantum fields using localized detectors, providing a relativistic update rule for the field state that avoids known impossibility issues in quantum field measurement.

Contribution

It introduces a detector-based measurement framework for quantum fields with an information-theoretic update rule, addressing previous limitations in quantum field measurement theory.

Findings

Defines a POVM induced by localized detectors in quantum fields

Provides a relativistic analogue of the L"uders update rule

Avoids the 'impossible measurements' problem in quantum field theory

Abstract

We propose a measurement theory for quantum fields based on measurements made with localized non-relativistic systems that couple covariantly to quantum fields (like the Unruh-DeWitt detector). Concretely, we analyze the positive operator-valued measure (POVM) induced on the field when an idealized measurement is carried out on the detector after it coupled to the field. Using an information-theoretic approach, we provide a relativistic analogue to the quantum mechanical L\"uders update rule to update the field state following the measurement on the detector. We argue that this proposal has all the desirable characteristics of a proper measurement theory. In particular it does not suffer from the "impossible measurements" problem pointed out by Rafael Sorkin in the 90s which shows that idealized measurements cannot be used in quantum field theory.