Quantum Field Measurements in the Fewster-Verch Framework

Abstract: The Fewster-Verch (FV) framework was introduced as a prescription to define local operations within a quantum field theory (QFT) that are free from Sorkin-like causal paradoxes. In this framework the measurement device is modeled via a probe QFT that, after interacting with the target QFT, is subject to an arbitrary local measurement. While the FV framework is rich enough to carry out quantum state tomography, it has two drawbacks. First, it is unclear if the FV framework allows conducting arbitrary local measurements. Second, if the probe field is interpreted as physical and the FV framework as fundamental, then one must demand the probe measurement to be itself implementable within the framework. That would involve a new probe, which should also be subject to an FV measurement, and so on. It is unknown if there exist non-trivial FV measurements for which such an "FV-Heisenberg cut" can be moved arbitrarily far away. In this work, we advance the first problem by proving that measurements of locally smeared fields fit within the FV framework. We solve the second problem by showing that any such field measurement admits a movable FV-Heisenberg cut.