Generalization of weak and non-selective measurements to QFT

Determine whether and how weak measurement and non-selective measurement schemes from non-relativistic quantum mechanics generalize to relativistic quantum field theory, and establish interpretations that preserve their intended non-invasive characteristics within QFT.

Background

The author notes that certain measurement strategies (weak and non-selective measurements) in non-relativistic quantum mechanics may be interpreted as minimally disturbing the system while providing state information.

However, measurement theory in QFT is still under active development, and it is unclear whether these strategies carry over to QFT, or how they should be interpreted in the relativistic field-theoretic context. This uncertainty impacts arguments about state information and coarse-graining.

References

given that measurement theory in QFT remains a difficult topic (Papageorgiou and Fraser, 2024), it isn’t clear that such things generalize to QFT, or that they can be interpreted in the same way in QFT.

— Quantum Field Theory and the Limits of Reductionism  (2407.20457 - Adlam, 2024) in Section 4.3, Dynamics Versus States

The weak values behave locally in the sense that the value for a certain qubit is undisturbed by a gate acting on other qubits, but it has not been shown that they conform to the continuous action condition for a general circuit, i.e.,~that they result in an SLGF model.

— Ontic and epistemic states in the theory of spacetime-local beables  (2609.00848 - Argaman, 1 Sep 2026) in Section 2.3, subsection “Other Stochastic Approaches”