Speed limits and locality in many-body quantum dynamics

TL;DR

This paper reviews mathematical speed limits in many-body quantum dynamics, focusing on Lieb-Robinson bounds and their extensions, highlighting key developments, results, and open questions in the field.

Contribution

It provides a comprehensive overview of Lieb-Robinson bounds, their extensions, and applications in quantum information and many-body physics, including self-contained proofs for newcomers.

Findings

Lieb-Robinson bounds establish finite speed of information propagation in quantum systems.

Extensions of bounds apply to systems with power-law interactions and models related to quantum gravity.

The paper highlights open questions and future directions in quantum speed limits.

Abstract

We review the mathematical speed limits on quantum information processing in many-body systems. After the proof of the Lieb-Robinson Theorem in 1972, the past two decades have seen substantial developments in its application to other questions, such as the simulatability of quantum systems on classical or quantum computers, the generation of entanglement, and even the properties of ground states of gapped systems. Moreover, Lieb-Robinson bounds have been extended in non-trivial ways, to demonstrate speed limits in systems with power-law interactions or interacting bosons, and even to prove notions of locality that arise in cartoon models for quantum gravity with all-to-all interactions. We overview the progress which has occurred, highlight the most promising results and techniques, and discuss some central outstanding questions which remain open. To help bring newcomers to the field up to speed, we provide self-contained proofs of the field's most essential results.