Related papers: Time Independence Does Not Limit Information Flow.…
The Lieb-Robinson bound (LRB) states that the range and strength of interactions between the constituents of a complex many-body system impose upper limits to how fast the signal can propagate. It manifests in a light cone-like growth of…
This is an introductory text reviewing Lieb-Robinson bounds for open and closed quantum many-body systems. We introduce the Heisenberg picture for time-dependent local Liouvillians and state a Lieb-Robinson bound that gives rise to a…
The dynamics of quantum systems strongly depends on the local structure of the Hamiltonian. For short-range interacting systems, the well-known Lieb-Robinson bound defines the effective light cone with an exponentially small error with…
We study general lattice bosons with long-range hopping and long-range interactions decaying as $|x-y|^{-\alpha} $ with $\alpha\in (d+2,2d+1)$. We find a linear light cone for the information propagation starting from suitable initial…
We describe an efficient protocol to perform quantum state transfer using Hamiltonian dynamics with long-range interactions. The time to transfer $n$ qubits a sufficiently large distance is proportional to $\sqrt{n}$. Even without error…
We introduce state-independent, non-perturbative Hamiltonian quantum speed limits for population leakage and fidelity loss, for a gapped open system interacting with a reservoir. These results hold in the presence of initial correlations…
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 approximately restricted inside the effective light cone that is…
Strongly long-range interacting quantum systems---those with interactions decaying as a power-law $1/r^{\alpha}$ in the distance $r$ on a $D$-dimensional lattice for $\alpha\le D$---have received significant interest in recent years. They…
We propose a general and experimentally accessible framework to quantify transition timing in discrete quantum systems via the time-of-flow (TF) distribution. Defined from the rate of population change in a target state, the TF distribution…
Quantum speed limits provide upper bounds on the rate with which a quantum system can move away from its initial state. Here, we provide a different kind of speed limit, describing the divergence of a perturbed open system from its…
Tracking the time evolution of a quantum state allows one to verify the thermalization rate or the propagation speed of correlations in generic quantum systems. Inspired by the energy-time uncertainty principle, bounds have been…
Judging by the enormous body of work that it has inspired, Elliott Lieb and Derek Robinson's 1972 article on the "Finite Group Velocity of Quantum Spin Systems" can be regarded as a \emph{high-impact paper}, as research accountants say. But…
The Lieb-Robinson (LR) bound rigorously shows that in quantum systems with short-range interactions, the maximum amount of information that travels beyond an effective "light cone" decays exponentially with distance from the light-cone…
The propagation of information in non-relativistic quantum systems obeys a speed limit known as a Lieb-Robinson bound. We derive a new Lieb-Robinson bound for systems with interactions that decay with distance $r$ as a power law,…
In this paper, we derive sharp lower bounds, also known as quantum speed limits, for the time it takes to transform a quantum system into a state such that an observable assumes its lowest average value. We assume that the system is…
Quantum speed limits set the maximal pace of state evolution. Two well-known limits exist for a unitary time-independent Hamiltonian: the Mandelstam-Tamm and Margolus-Levitin bounds. The former restricts the rate according to the state…
Extending the quantum formulation of [Phys. Rev. X 3, 041003 (2013)] to a more general setting for studying the thermodynamics of information processing including initial correlations, we generalize the second law of thermodynamics to…
We consider the time-dependent Schr\"odinger equation that is generated on the bosonic Fock space by a long-range quantum many-body Hamiltonian. We derive the first bound on the maximal speed of particle transport in these systems that is…
The Lieb-Robinson bound states that local Hamiltonian evolution in nonrelativistic quantum mechanical theories gives rise to the notion of an effective light-cone with exponentially decaying tails. We discuss several consequences of this…
In this work, we investigate how quickly local perturbations propagate in interacting boson systems with Bose-Hubbard-type Hamiltonians. In general, these systems have unbounded local energies, and arbitrarily fast information propagation…