Factorisation conditions and causality for local measurements in QFT

Quantum operations that are perfectly admissible in non-relativistic quantum theory can enable signalling between spacelike separated regions when naively imported into quantum field theory (QFT). Prominent examples of such “impossible measurements”, in the sense of Sorkin, include certain unitary kicks and projective measurements. It is generally accepted that only those quantum operations whose physical implementation arises from a fully relativistically covariant interaction, between the quantum field and a suitable probe, should be regarded as admissible. While this idea has been realised at the level of abstract algebraic QFT, or via particular measurement models, there is still no general set of operational criteria characterising which measurements are physically implementable. In this work we adopt the local S-matrix formalism, and make use of a hierarchy of factorisation conditions that exclude both superluminal signalling and retrocausality, thereby providing such a criterion. Realising the local S-matrices through explicit interactions between smeared field operators and a pointer degree of freedom, we further derive local causality conditions for the induced Kraus operators, which guarantee the absence of signalling in “impossible measurement” scenarios. Finally, we show that the accuracy with which local field observables can be measured is fundamentally limited by the retarded propagator of the field, which also plays an essential role in a factorisation identity we prove for the field Kraus operators.

💡 Research Summary

The paper addresses a long‑standing puzzle in relativistic quantum field theory (QFT): operations that are perfectly legitimate in non‑relativistic quantum mechanics can, when naively transplanted into QFT, enable super‑luminal signalling between spacelike separated regions. Classic examples of such “impossible measurements” (in Sorkin’s terminology) include certain unitary “kicks” and ideal projective measurements followed by the Lüders state‑update rule. The authors argue that only operations that arise from fully covariant interactions between the field and a physical probe should be regarded as admissible. While algebraic QFT and specific measurement models have illustrated this point, a general operational criterion has been missing.

To fill this gap the authors adopt the local S‑matrix formalism pioneered by Bogoliubov and Stueckelberg. A local S‑matrix S