(PhD Thesis) The Information Locally Stored in Quantum Fields: From Entanglement to Gravity

TL;DR

This work develops a local, operational picture of quantum fields by treating localized quantum fields as probes and by analyzing how information about entanglement and spacetime geometry is stored and extractable from quantum fields. It unifies foundational algebraic quantum field theory with practical detector models, notably Unruh–DeWitt detectors, via the Fewster–Verch measurement framework, and shows how localized probes access field correlations while respecting relativistic causality. A central result is that entanglement between finite spacetime regions can be quantified both from field degrees of freedom and via detector harvesting, with clear regimes where mediator quantum degrees of freedom are essential or effectively negligible. The thesis further demonstrates that spacetime geometry is fully encoded in quantum-field correlations (Hadamard structure and two-point functions) and that local measurements can, in principle, reconstruct the background metric, raising the possibility that gravity could emerge from quantum-field entanglement. Collectively, these insights pave the way for concrete protocols to probe quantum fields in curved spacetimes and to explore gravity–quantum-field interplays using realistic, localized detectors.

Abstract

This is an updated version of my PhD thesis, defended at the University of Waterloo on the 2nd of April 2025, uploaded to the ArXiv with the goal of reaching a wider audience. The thesis is divided into 5 chapters, respectively containing (I) a brief introduction to local quantum field theory (QFT), (II) a description of local probes in QFT, (III) a discussion of entanglement in QFT and how to probe it, (IV) a description of the regimes where QFT interactions can be approximated by direct interactions, and (V) a discussion the information about the geometry of spacetime contained in quantum fields. The partial goal of this thesis is to serve as a guide for students aiming to tackle these different research programs. If the reader is interested in pursuing one or more research projects detailed here, they are encouraged to contact me for collaboration in these topics.

Figures (34)

• Figure 1: Schematic representation of a spacetime diagram of the setup considered by Sorkin in Sorkin.
• Figure 2: Schematic representation of a spacetime diagram of the setup considered in impossible.
• Figure 3: The two-level Unruh-DeWitt detector's leading order excitation probability as a function of $\Omega T$ for different values of $\sigma$.
• Figure 4: Schematic representation of the region delimited by the $\tau$-Fermi bound (in yellow) within each constant $\tau$ surface $\Sigma_\tau$ (in gray).
• Figure 5: Fermi normal coordinates for a uniformly accelerated trajectory in Minkowski spacetime.