Signaling and Scrambling with Strongly Long-Range Interactions

Abstract

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 are present in leading experimental platforms for quantum computation and simulation, as well as in theoretical models of quantum information scrambling and fast entanglement creation. Since no notion of locality is expected in such systems, a general understanding of their dynamics is lacking. As a first step towards rectifying this problem, we prove two new Lieb-Robinson-type bounds that constrain the time for signaling and scrambling in strongly long-range interacting systems, for which no tight bounds were previously known. Our first bound applies to systems mappable to free-particle Hamiltonians with long-range hopping, and is saturable for $\alpha \le D/2$. Our second bound pertains to generic long-range interacting spin Hamiltonians, and leads to a tight lower bound for the signaling time to extensive subsets of the system for all $\alpha <D$. This result also lower-bounds the scrambling time, and suggests a path towards achieving a tight scrambling bound that can prove the long-standing fast scrambling conjecture.

arXiv comment$5+\epsilon +5$ pages, $1+2$ figures

References in corpus (45)

• Quantum information with Rydberg atoms
• Many body localization and thermalization in quantum statistical mechanics
• A bound on chaos
• Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
• Black holes and the butterfly effect
• Black holes as mirrors: quantum information in random subsystems
• Fast Scramblers
• An Area Law for One Dimensional Quantum Systems
• Observation of discrete time-crystalline order in a disordered dipolar many-body system
• Engineered 2D Ising interactions on a trapped-ion quantum simulator with hundreds of spins
• Realizing a lattice spin model with polar molecules
• Operator Spreading in Random Unitary Circuits
• Chaos in quantum channels
• Measuring out-of-time-order correlations and multiple quantum spectra in a trapped ion quantum magnet
• Spectral Gap and Exponential Decay of Correlations
• Operator hydrodynamics, OTOCs, and entanglement growth in systems without conservation laws
• Quantum many-body models with cold atoms coupled to photonic crystals
• Emergence and Frustration of Magnetic Order with Variable-Range Interactions in a Trapped Ion Quantum Simulator
• Towards the fast scrambling conjecture
• Local criticality, diffusion and chaos in generalized Sachdev-Ye-Kitaev models
• Topological quantum order: stability under local perturbations
• Spread of correlations in long-range interacting quantum systems
• Lieb-Robinson and the butterfly effect
• Scalable Architecture for a Room Temperature Solid-State Quantum Information Processor
• Nearly-linear light cones in long-range interacting quantum systems
• Scrambling and entanglement spreading in long-range spin chains
• Operator growth in the SYK model
• Breakdown of quasilocality in long-range quantum lattice models
• Persistence of locality in systems with power-law interactions
• Diverging equilibration times in long-range quantum spin models
• Locality, Quantum Fluctuations, and Scrambling
• Entanglement area laws for long-range interacting systems
• Universal Scaling Laws for Correlation Spreading in Quantum Systems with Short- and Long-Range Interactions
• Dynamical critical scaling of long-range interacting quantum magnets
• Locality and digital quantum simulation of power-law interactions
• Cooperative shielding in many-body systems with long-range interaction
• Fast State Transfer and Entanglement Renormalization Using Long-Range Interactions
• Fast scrambling on sparse graphs
• Quantum chaos dynamics in long-range power law interaction systems
• New dynamical scaling universality for quantum networks across adiabatic quantum phase transitions
• Emergent locality in systems with power-law interactions
• Interplay of Soundcone and Supersonic Propagation in Lattice Models with Power Law Interactions
• Quantum Speed Limits for Quantum Information Processing Tasks
• Quantum Causal Influence
• $N$-Scaling of Timescales in Long-Range $N$-Body Quantum Systems

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• Programmable Quantum Simulations of Spin Systems with Trapped Ions
• Long-range interacting quantum systems
• Challenges to observation of many-body localization
• Polynomially filtered exact diagonalization approach to many-body localization
• The Lieb-Robinson light cone for power-law interactions
• Out-of-equilibrium dynamics of quantum many-body systems with long-range interactions
• Speed limits and locality in many-body quantum dynamics
• Absence of fast scrambling in thermodynamically stable long-range interacting systems
• Tightening the Lieb-Robinson Bound in Locally-Interacting Systems
• Strong quantum metrological limit from many-body physics
• Dynamical Phase Transitions in models of Collective Neutrino Oscillations
• Optimal State Transfer and Entanglement Generation in Power-law Interacting Systems
• Bound on quantum scrambling with all-to-all interactions
• Lieb Robinson bounds and out of time order correlators in a long range spin chain
• Quantum chaos and ensemble inequivalence of quantum long-range Ising chains
• Dynamical scaling of correlations generated by short- and long-range dissipation
• Finite speed of quantum information in models of interacting bosons at finite density
• Advantages and limitations of quantum routing
• Complexity phase diagram for interacting and long-range bosonic Hamiltonians
• Catching thermal avalanches in the disordered XXZ model
• Implementing two-qubit gates at the quantum speed limit
• Energy-Resolved Information Scrambling in Energy-Space Lattices
• Quantum delocalization on correlation landscape: The key to exponentially fast multipartite entanglement generation
• Fast high-fidelity multi-qubit state transfer with long-range interactions
• Fast and Accurate Greenberger-Horne-Zeilinger Encoding Using All-to-all Interactions
• Information Scrambling and the Correspondence of Entanglement- and Operator Dynamics in Systems with Nonlocal Interactions
• Causality, localization, and universality of monitored quantum walks with long-range hopping
• Time optimal quantum state transfer in a fully-connected quantum computer
• Aspects of entanglement in non-local field theories with fractional Laplacian
• Quantum Chaos, Randomness and Universal Scaling of Entanglement in Various Krylov Spaces
• Fast and efficient long-distance quantum state transfer in long-range spin-$\frac{1}{2}$ models
• Frobenius light cone and the shift unitary
• Implementing a Fast Unbounded Quantum Fanout Gate Using Power-Law Interactions
• Macroscopic Particle Transport in Dissipative Long-Range Bosonic Systems
• Measurement-induced criticality in extended and long-range unitary circuits
• Delocalized Excitation Transfer in Open Quantum Systems with Long-Range Interactions
• Lieb-Robinson bounds with exponential-in-volume tails