Aspects of Quantum Information in Quantum Field Theory: Particle detector models, entanglement, and complexity

Abstract

This thesis explores three themes in the interface between quantum information and quantum field theory (QFT). Part 1 is devoted to particle detector models, which are one of the key ingredients in formulations of a measurement theory for quantum fields. In tune with recent efforts to devise a fully local and relativistic measurement theory for quantum fields, we present a simple model of a local probe that is, itself, formulated in terms of a field theory. We then proceed to show how to systematically reduce this field-theoretic description of the probe to an effective theory restricted to a finite set of modes. The resulting dynamics at leading order in perturbation theory are given precisely by the widely adopted models for detectors based on nonrelativistic probe systems. These results pave the way to bridge the gap between the fully field-theoretic and the detector-based approach to measurements in QFT, and give particle detector models an effective field theory flavor. Part 2 then focuses on the concept of entanglement in quantum field theory. We start in the first half of Part 2 by studying a protocol known as entanglement harvesting, which allows two localized probes to extract entanglement from a quantum field even before they have time to exchange causal signals. Recent works on field-theoretic models for local probes in relativistic quantum information have raised objections against the possibility of entanglement harvesting at weak coupling between the probes and the field when the probes themselves consist of localized degrees of freedom of a field theory. We address the origins of these concerns and show that, for an appropriate choice of modes used as probes for the quantum field, it is indeed possible to harvest entanglement using localized probes described along the lines of the formalism presented in Part 1. In the second half of Part 2, we also show how to best couple to a quantum field in order to most accurately reproduce its entanglement structure. This helps to establish limits on how efficient entanglement harvesting between complementary subregions can be, and also suggests further directions for how to address the problem of probing the structure of entanglement in field theory in more general scenarios. Finally, in Part 3, we delve into the concept of computational complexity of Gaussian states, which are a special class of quantum states that is pervasive in many contexts in QFT. Following Nielsen's geometric approach to circuit complexity, we devise a general class of metrics on the space of Gaussian unitary circuits which allows the circuit complexity of any pure Gaussian state to be characterized in a unified fashion. This gives us a generalized framework that can accommodate additional physical constraints on the notion of complexity adopted; we comment on a few examples where these additional features can be of physical relevance.