Related papers: Locality and error correction in quantum dynamics …
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…
The Lieb-Robinson bound shows the existence of a maximum speed of signal propagation in discrete quantum mechanical systems with local interactions. This generalizes the concept of relativistic causality beyond field theory, and provides a…
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,…
Lieb-Robinson bounds show that the speed of propagation of information under the Heisenberg dynamics in a wide class of non-relativistic quantum lattice systems is essentially bounded. We review work of the past dozen years that has turned…
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…
We study equilibration of an isolated quantum system by mapping it onto a network of classical oscillators in Hilbert space. By choosing a suitable basis for this mapping, the degree of locality of the quantum system reflects in the…
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 on information propagation in quantum systems with power-law…
We revisit key notions related to the evolution of quantum information in few-body quantum mechanics (fbQM) and, for a wide class of dispersion relations, prove uniform bounds on the maximal speed of propagation of quantum information for…
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…
The Lieb-Robinson bound shows that the speed of propagating information in a nonrelativistic quantum lattice system is bounded by a finite velocity, which entails the clustering of correlations. In this paper, we extend the Lieb-Robinson…
We propose new Lieb-Robinson bounds (bounds on the speed of propagation of information in quantum systems) with an explicit dependence on the interaction strengths of the Hamiltonian. For systems with more than two interactions it is found…
We study the velocity of the propagation of information for a class of local dissipative quantum dynamics. This finite velocity is expressed by the so-called Lieb-Robinson bound. Besides the properties of the already studied dynamics, we…
We review various bounds concerning out-of-equilibrium dynamics in few-level and many-body quantum systems. We primarily focus on closed quantum systems but will also mention some related results for open quantum systems and classical…
Quantum many-body interactions can induce quantum entanglement among particles, rendering them valuable resources for quantum-enhanced sensing. In this work, we derive a universal and fundamental bound for the growth of the quantum Fisher…
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…
The speed of information propagation in long-range interacting quantum systems is limited by Lieb-Robinson-type bounds, whose tightness can be established by finding specific quantum state-transfer protocols. Previous works have given…
Speed of state transitions in macroscopic systems is a crucial concept for foundations of nonequilibrium statistical mechanics as well as various applications in quantum technology represented by optimal quantum control. While extensive…
These lecture notes focus on the application of ideas of locality, in particular Lieb-Robinson bounds, to quantum many-body systems. We consider applications including correlation decay, topological order, a higher dimensional…
We show that, assuming that quantum mechanics holds locally, the finite speed of information is the principle that limits all possible correlations between distant parties to be quantum mechanical as well. Local quantum mechanics means that…
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…