Causal State Updates in Real Scalar Quantum Field Theory

Understand

In relativistic Quantum Field Theory (QFT) ideal measurements of certain observables are physically impossible without violating causality.

• This prompts two questions: i) can a given observable be ideally measured in QFT, and ii) if not, in what sense can it be measured? Here we formulate a necessary and sufficient condition that any measurement, and more generally any state update (quantum operation), must satisfy to respect causality in real scalar QFT.
• We argue that for unitary `kicks' and operations involving 1-parameter families of Kraus operators, e.g.
• Gaussian measurements, the only causal observables are smeared fields and the identity -- the basic observables in real scalar QFT.