Measurements of quantum fields with particle detectors

Abstract

This thesis aims to provide a working measurement theory for quantum fields built upon measurements using localized non-relativistic quantum systems, widely known as particle detectors.

In Chapters 3 to 5, we focus on using detector-based schemes to carefully formulate a measurement theory that is compatible with relativity. To do so, we provide a rigorous analysis of the causal behaviour of the induced non-selective channels, as well as an update rule that is consistent with relativistic causality. In the process, we establish a body of results, including a characterization of localized causal channels in real scalar QFT, and the formulation of a formalism that allows a consistent treatment of non-relativistic multipartite systems in relativistic setups.

In Chapters 6 to 8, we focus on verifying that the measurement theory formulated in the first part is a working measurement theory, meaning that it can actually be used in practice to measure specific targeted features of the quantum field. To ensure this, we introduce a measurement strategy where particle detectors always undergo the same measurement protocol—regardless of the quantity or feature of interest—and then are subjected to a tomography process. The resulting data is fed into a trained neural network that is capable of inferring the targeted quantity or feature from the detector's readings. This strategy has the potential to be applicable to measure any quantity of the field that is accessible through local measurements. More tangentially, we also introduce a method beyond perturbation theory that uses trains of delta couplings to efficiently approximate the final state of a detector undergoing a continuous interaction. Additionally, we apply the detector-based measurement theory to analyze the effect of measurements on the protocol of entanglement harvesting.