Factorisation conditions and causality for local measurements in QFT

TL;DR

This paper establishes operational criteria for physically admissible measurements in quantum field theory, ensuring no superluminal signalling and causality violations, by using local S-matrix formalism and factorisation conditions.

Contribution

It introduces a hierarchy of factorisation conditions within the local S-matrix framework to characterize physically implementable measurements in QFT.

Findings

Factorisation conditions exclude superluminal signalling.

Local causality conditions guarantee measurement locality.

Measurement accuracy is limited by the field's retarded propagator.

Abstract

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.