Abstract: I will present a recently developed formalism for quantum measurements that is both technically powerful and conceptually transparent. This framework is the basis for new results based on condensed matter principles like locality and universality that were not previously thought possible—including extending the Lieb-Robinson Theorem to dynamics with measurements and proving deep connections between measurement-based quantum computation and topological order. In contrast to the conventional wisdom that measurements destroy locality, we find a maximum enhancement to the speed of quantum information in measurement-assisted protocols, establishing a precise notion of locality. I’ll discuss the formal resolution to the EPR paradox, constraints on quantum teleportation, error correction, routing, and the preparation of useful resource states (e.g., Bell, GHZ, Dicke, and squeezed states). I’ll present optimal quantum protocols that achieve these tasks, reveal new resource tradeoffs, and discuss important implications for measurement-based quantum computing and its fundamental connection to symmetry-protected topological order. Finally, I'll comment on other applications relevant to condensed matter and future applications of this work.