The vision of quantum information science and technology (QIST) is to process information with quantum interactions, performing computational logic with improved efficiency via the unique non-local correlations---entanglement---permeating many-body quantum systems. As such, entanglement is a critical resource for all applications of quantum devices, promoting them to be exponentially more complex than the sum of their individual parts. While the technology of quantum computing is rapidly progressing, practical insight into correspondingly large-scale entanglement has remained challenging, especially in the context of more than a few qubits (or qudits, modes, etc.) and in the presence of realistic noisy experimental environments. This program responds to this challenge by leveraging quantum fields as a guide to new theory and calculation techniques that specifically focus on the scalable entanglement structures found in our fundamental descriptions of the particles and forces of Nature. Beyond critical resource characterization, this research is positioned to connect with distributed quantum sensing, to impact our designs of quantum simulations relevant to collider experiments, and to guide hardware specifications of modular quantum architectures for scientific applications in subatomic physics. The study of mixed-state entanglement structure between detectors at spacelike separations in the free scalar field vacuum has introduced new computational tools to the many-b