Hierarchy of linear light cones with long-range interactions

Abstract

In quantum many-body systems with local interactions, quantum information and entanglement cannot spread outside of a linear light cone, which expands at an emergent velocity analogous to the speed of light. Local operations at sufficiently separated spacetime points approximately commute -- given a many-body state, ${\mathcal{O}}_x(t){\mathcal{O}}_y|\psi ⟩\approx {\mathcal{O}}_y{\mathcal{O}}_x(t)|\psi ⟩$ with arbitrarily small errors -- so long as $|x-y|\gtrsim vt$, where $v$ is finite. Yet most non-relativistic physical systems realized in nature have long-range interactions: two degrees of freedom separated by a distance $r$ interact with potential energy $V(r)\propto 1/r^{\alpha }$. In systems with long-range interactions, we rigorously establish a hierarchy of linear light cones: at the same $\alpha$, some quantum information processing tasks are constrained by a linear light cone while others are not. In one spatial dimension, this linear light cone exists for every many-body state when $\alpha >3$ (Lieb-Robinson light cone); for a typical state chosen uniformly at random from the Hilbert space when $\alpha >\frac{5}{2}$ (Frobenius light cone); for every state of a non-interacting system when $\alpha >2$ (free light cone). These bounds apply to time-dependent systems and are optimal up to subalgebraic improvements. Our theorems regarding the Lieb-Robinson and free light cones -- and their tightness -- also generalize to arbitrary dimensions. We discuss the implications of our bounds on the growth of connected correlators and of topological order, the clustering of correlations in gapped systems, and the digital simulation of systems with long-range interactions. In addition, we show that universal quantum state transfer, as well as many-body quantum chaos, are bounded by the Frobenius light cone, and therefore are poorly constrained by all Lieb-Robinson bounds.

arXiv comment36 pages; 6 figures; v2: revised and expanded introduction, a few extra results; v3: minor revisions. v4: corrections in Section 7

References in corpus (41)

• The Large N Limit of Superconformal Field Theories and Supergravity
• Quantum information with Rydberg atoms
• A bound on chaos
• Quantum state transfer and entanglement distribution among distant nodes in a quantum network
• Black holes and the butterfly effect
• An Area Law for One Dimensional Quantum Systems
• Engineered 2D Ising interactions on a trapped-ion quantum simulator with hundreds of spins
• Realizing a lattice spin model with polar molecules
• Bose-Einstein Condensation of Erbium
• Non-local propagation of correlations in long-range interacting quantum systems
• Lieb-Robinson bounds and the generation of correlations and topological quantum order
• Measuring out-of-time-order correlations and multiple quantum spectra in a trapped ion quantum magnet
• Spectral Gap and Exponential Decay of Correlations
• Quantum many-body models with cold atoms coupled to photonic crystals
• Experimental Comparison of Two Quantum Computing Architectures
• Floquet-Magnus Theory and Generic Transient Dynamics in Periodically Driven Many-Body Quantum Systems
• Exponentially slow heating in periodically driven many-body systems
• Measuring out-of-time-order correlators on a nuclear magnetic resonance quantum simulator
• Verified Quantum Information Scrambling
• A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems
• Scalable Architecture for a Room Temperature Solid-State Quantum Information Processor
• Nearly-linear light cones in long-range interacting quantum systems
• The Dynamics of 1D Quantum Spin Systems Can Be Approximated Efficiently
• Persistence of locality in systems with power-law interactions
• Finite speed of quantum scrambling with long range interactions
• Strictly linear light cones in long-range interacting systems of arbitrary dimensions
• Entanglement area laws for long-range interacting systems
• Locality and digital quantum simulation of power-law interactions
• Topological phases with long-range interactions
• Fast State Transfer and Entanglement Renormalization Using Long-Range Interactions
• An improved Lieb-Robinson bound for many-body Hamiltonians with power-law interactions
• Robust spin squeezing via photon-mediated interactions on an optical clock transition
• Quantum chaos dynamics in long-range power law interaction systems
• The operator Lévy flight: light cones in chaotic long-range interacting systems
• Emergent locality in systems with power-law interactions
• Dynamical phase transitions in sampling complexity
• Parallel time-dependent variational principle algorithm for matrix product states
• Quantum Speed Limits for Quantum Information Processing Tasks
• Engineering spin squeezing in a 3D optical lattice with interacting spin-orbit-coupled fermions
• Locality and Heating in Periodically Driven, Power-law Interacting Systems
• Quantum computational supremacy in the sampling of bosonic random walkers on a one-dimensional lattice

Cited by in corpus (74)

• Programmable Quantum Simulations of Spin Systems with Trapped Ions
• Long-range interacting quantum systems
• Provably efficient machine learning for quantum many-body problems
• Fate of measurement-induced phase transition in long-range interactions
• Strictly linear light cones in long-range interacting systems of arbitrary dimensions
• Scrambling Dynamics and Out-of-Time Ordered Correlators in Quantum Many-Body Systems: a Tutorial
• The Lieb-Robinson light cone for power-law interactions
• Many-body quantum teleportation via operator spreading in the traversable wormhole protocol
• Speed limits and locality in many-body quantum dynamics
• Asymmetric blockade and multi-qubit gates via dipole-dipole interactions
• Absence of fast scrambling in thermodynamically stable long-range interacting systems
• Lieb-Robinson bound and almost-linear light-cone in interacting boson systems
• Quantum heat engine with long-range advantages
• Optimal State Transfer and Entanglement Generation in Power-law Interacting Systems
• Quantum operator growth bounds for kicked tops and semiclassical spin chains
• Quantum Error Mitigated Classical Shadows
• Spreading of Correlations and Entanglement in the Long-Range Transverse Ising Chain
• Bound on quantum scrambling with all-to-all interactions
• Many-body quantum dynamics slows down at low density
• Lieb Robinson bounds and out of time order correlators in a long range spin chain
• Dynamical scaling of correlations generated by short- and long-range dissipation
• Finite speed of quantum information in models of interacting bosons at finite density
• Operator growth bounds from graph theory
• Long-Range Free Fermions: Lieb-Robinson Bound, Clustering Properties, and Topological Phases
• Optimal Frobenius light cone in spin chains with power-law interactions
• Non-perturbative dynamics of the operator size distribution in the Sachdev-Ye-Kitaev model
• Entanglement Phases in large-N hybrid Brownian circuits with long-range couplings
• Exponential clustering of bipartite quantum entanglement at arbitrary temperatures
• Prethermalization and the local robustness of gapped systems
• Complexity phase diagram for interacting and long-range bosonic Hamiltonians
• Fractal nature of high-order time crystal phases
• Implementing two-qubit gates at the quantum speed limit
• Bound state dynamics in the long-range spin-$\frac{1}{2}$ XXZ model
• Ion Trap Long-Range XY Model for Quantum State Transfer and Optimal Spatial Search
• Dilute measurement-induced cooling into many-body ground states
• Fast high-fidelity multi-qubit state transfer with long-range interactions
• Topological to magnetically ordered quantum phase transition in antiferromagnetic spin ladders with long-range interactions
• Disordered Lieb-Robinson bounds in one dimension
• Inhomogeneity induced shortcut to adiabaticity in Ising chains with long-range interactions
• Information Scrambling and the Correspondence of Entanglement- and Operator Dynamics in Systems with Nonlocal Interactions
• Fast and Accurate Greenberger-Horne-Zeilinger Encoding Using All-to-all Interactions
• Impact of dephasing on non-equilibrium steady-state transport in fermionic chains with long-range hopping
• Bounding the finite-size error of quantum many-body dynamics simulations
• Optimal light cone for macroscopic particle transport in long-range systems: A quantum speed limit approach
• From decay of correlations to locality and stability of the Gibbs state
• Causality, localization, and universality of monitored quantum walks with long-range hopping
• Mimicking quantum correlation of a long-range Hamiltonian by finite-range interactions
• The Measurement-induced Transition in Long-range Interacting Quantum Circuits
• Stabilization of Discrete Time-Crystaline Response on a Superconducting Quantum Computer by increasing the Interaction Range
• Rise and fall of entanglement between two qubits in a non-Markovian bath
• Time optimal quantum state transfer in a fully-connected quantum computer
• Solving Free Fermion Problems on a Quantum Computer
• Quantum teleportation implies symmetry-protected topological order
• Locality of gapped ground states in systems with power-law decaying interactions
• From Light-Cone to Supersonic Propagation of Correlations by Competing Short- and Long-Range Couplings
• Optimal spatial searches with long-range tunneling
• Enhanced Lieb-Robinson bounds for commuting long-range interactions
• Frobenius light cone and the shift unitary
• Sub-ballistic operator growth in spin chains with heavy-tailed random fields
• Tighter Lower Bounds on Quantum Annealing Times
• Efficient Learning of Long-Range and Equivariant Quantum Systems
• Implementing a Fast Unbounded Quantum Fanout Gate Using Power-Law Interactions
• Lieb-Robinson correlation function for the quantum transverse field Ising model
• Tailoring interaction ranges in atom arrays
• Dynamics and steady states of tight-binding chains in presence of isolated defects
• Stability of thermal equilibrium in long-range quantum systems
• Quantum Mechanics and the Continuum Limit of an Emergent Geometry
• Out-of-time-order correlator computation based on discrete truncated Wigner approximation
• Lieb-Robinson bounds with exponential-in-volume tails
• Lieb-Robinson bounds imply locality of interactions
• Spread of Correlations in Strongly Disordered Lattice Systems with Long-Range Coupling
• Expediting quantum state transfer through the long-range extended XY model
• Optimal quantum spatial search with one-dimensional long-range interactions
• Revealing effects of local dimension on variable-range interacting model by connecting Lieb-Robinson bounds and multipartite entanglement