Entanglement of Local Operators and the Butterfly Effect
arXiv:2005.14243 · doi:10.1103/PhysRevResearch.3.033182
Abstract
We study the robustness of quantum and classical information to perturbations implemented by local operator insertions. We do this by computing multipartite entanglement measures in the Hilbert space of local operators in the Heisenberg picture. The sensitivity to initial conditions that we explore is an illuminating manifestation of the butterfly effect in quantum many-body systems. We derive a "membrane theory" in Haar random unitary circuits to compute the mutual information, logarithmic negativity, and reflected entropy in the local operator state by mapping to a classical statistical mechanics problem and find that any local operator insertion delocalizes information as fast as is allowed by causality. Identical behavior is found for conformal field theories admitting holographic duals where the bulk geometry is described by the eternal black hole with a local object situated at the horizon. In contrast to these maximal scramblers, only an amount of information is found to be delocalized by local operators in integrable systems such as free fermions and Clifford circuits.
arXiv commentv2: Presentation improved, Appendix A revised
References in corpus (63)
- Holographic Derivation of Entanglement Entropy from AdS/CFT
- From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
- A bound on chaos
- A Stress Tensor for Anti-de Sitter Gravity
- Aspects of Holographic Entanglement Entropy
- Comments on the Sachdev-Ye-Kitaev model
- A Covariant Holographic Entanglement Entropy Proposal
- Holographic Reconstruction of Spacetime and Renormalization in the AdS/CFT Correspondence
- Black holes and the butterfly effect
- Evolution of Entanglement Entropy in One-Dimensional Systems
- Generalized gravitational entropy
- Operator Spreading in Random Unitary Circuits
- Chaos in AdS holography
- Chaos in quantum channels
- Quantum Entanglement Growth Under Random Unitary Dynamics
- Localized shocks
- Operator hydrodynamics, OTOCs, and entanglement growth in systems without conservation laws
- Entanglement and thermodynamics after a quantum quench in integrable systems
- Two-dimensional conformal field theory and the butterfly effect
- Local criticality, diffusion and chaos in generalized Sachdev-Ye-Kitaev models
- The Gravity Dual of Renyi Entropy
- Holographic Entanglement of Purification
- Virasoro Conformal Blocks and Thermality from Classical Background Fields
- Entanglement of Quantum Evolutions
- Emergent statistical mechanics of entanglement in random unitary circuits
- Entanglement dynamics after quantum quenches in generic integrable systems
- Out-of-time-order correlators in quantum mechanics
- Holographic Local Quenches and Entanglement Density
- Holographic Entanglement Entropy from 2d CFT: Heavy States and Local Quenches
- Exact dynamics in dual-unitary quantum circuits
- Operator space entanglement entropy in transverse Ising chain
- Entanglement Scrambling in 2d Conformal Field Theory
- Operator Entanglement in Interacting Integrable Quantum Systems: the Case of the Rule 54 Chain
- Entanglement scaling of operators: a conformal field theory approach, with a glimpse of simulability of long-time dynamics in 1+1d
- The entanglement membrane in chaotic many-body systems
- Quantum Dimension as Entanglement Entropy in 2D CFTs
- Operator Entanglement in Local Quantum Circuits I: Chaotic Dual-Unitary Circuits
- Scrambling in Random Unitary Circuits: Exact Results
- Operator entanglement entropy of the time evolution operator in chaotic systems
- Quantum Entanglement of Localized Excited States at Finite Temperature
- Operator Space Entanglement Entropy in XY Spin Chains
- Entanglement on mixed stabiliser states--I: Normal Forms and Reduction Procedures
- Entanglement Wedge Cross Section from CFT: Dynamics of Local Operator Quench
- Entanglement spectrum of random-singlet quantum critical points
- Scrambling time from local perturbations of the eternal BTZ black hole
- Light Cone Bootstrap in General 2D CFTs and Entanglement from Light Cone Singularity
- Operator Entanglement in Local Quantum Circuits II: Solitons in Chains of Qubits
- Correlation measures and the entanglement wedge cross-section after quantum quenches in two-dimensional conformal field theories
- Membrane theory of entanglement dynamics from holography
- Scrambling without chaos in RCFT
- Holographic entanglement negativity and replica symmetry breaking
- Unitary designs from statistical mechanics in random quantum circuits
- Entanglement Entropy, OTOC and Bootstrap in 2D CFTs from Regge and Light Cone Limits of Multi-point Conformal Block
- Lyapunov growth in quantum spin chains
- Quantum vs. classical information: operator negativity as a probe of scrambling
- Dynamics of Entanglement Wedge Cross Section from Conformal Field Theories
- Conformal field theory and the web of quantum chaos diagnostics
- Fractional Statistics and the Butterfly Effect
- Signature of quantum chaos in operator entanglement in 2d CFTs
- The quasi-particle picture and its breakdown after local quenches: mutual information, negativity, and reflected entropy
- Coarse-grained dynamics of operator and state entanglement
- Barrier from chaos: operator entanglement dynamics of the reduced density matrix
- Exploring the Membrane Theory of Entanglement Dynamics
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- Quantum Information in Holographic Duality
- Operator growth in 2d CFT
- Distinguishing Random and Black Hole Microstates
- Interplay between the Lyapunov exponents and phase transitions of charged AdS black holes
- Scrambling and Recovery of Quantum Information in Inhomogeneous Quenches in Two-dimensional Conformal Field Theories
- Reflected entropy is not a correlation measure
- Rényi Mutual Information in Quantum Field Theory
- Information Scrambling with Conservation Laws
- Information Scrambling Versus Quantum Revival Through the Lens of Operator Entanglement
- Topological Defects in Floquet Circuits
- Entanglement Dynamics of the Non-Unitary Holographic Channel
- Bridging Entanglement and Magic Resources within Operator Space
- Local Operator Entanglement in Spin Chains
- An Exact Link between Nonlocal Nonstabilizerness and Operator Entanglement
- Volume-law entanglement entropy of typical pure quantum states
- Logarithmic growth of operator entanglement in a clean non-integrable circuit