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 …

The Lieb-Robinson theorem states that information propagates with a finite velocity in
quantum systems on a lattice with nearest-neighbor interactions. What are the speed limits …

Conservation laws can constrain entanglement dynamics in isolated quantum systems,
manifest in a slowdown of higher Rényi entropies. Here, we explore this phenomenon in a …

The speed limit of information propagation is one of the most fundamental features in non-
equilibrium physics. The region of information propagation by finite-time dynamics is …

Quantum simulation has wide applications in quantum chemistry and physics. Recently,
scientists have begun exploring the use of randomized methods for accelerating quantum …

We present an optimal protocol for encoding an unknown qubit state into a multiqubit
Greenberger-Horne-Zeilinger-like state and, consequently, transferring quantum information …

We prove that quantum information propagates with a finite velocity in any model of
interacting bosons whose (possibly time-dependent) Hamiltonian contains spatially local …

A fundamental principle of many-body physics is causality: a strict prohibition of information
propagation outside the light cone. However, in non-relativistic systems, it is often unclear …

Let A and B be local operators in Hamiltonian quantum systems with N degrees of freedom
and finite-dimensional Hilbert space. We prove that the commutator norm‖[A (t), B]‖ is …

We bound the time necessary to implement the shift unitary on a one-dimensional ring, both
by using local Hamiltonians and those with power-law interactions. This time is constrained …