Local measures of entanglement in black holes and CFTs

Abstract

We study the structure and dynamics of entanglement in CFTs and black holes. We use a local entanglement measure, the entanglement contour, which is a spatial density function for von Neumann entropy with some additional properties. The entanglement contour can be calculated in many 1+1d condensed matter systems and simple models of black hole evaporation. We calculate the entanglement contour of a state excited by a splitting quench, and find universal results for the entanglement contours of low energy non-equilibrium states in 2d CFTs. We also calculate the contour of a non-gravitational bath coupled to an extremal AdS${}_2$ black hole, and find that the contour only has finite support within the bath, due to an island phase transition. The particular entanglement contour proposal we use quantifies how well the bath's state can be reconstructed from its marginals, through its connection to conditional mutual information, and the vanishing contour is a reflection of the protection of bulk island regions against erasures of the boundary state.

arXiv comment35 pages, 8 figures. v2: minor corrections and clarifications

References in corpus (45)

• Holographic Derivation of Entanglement Entropy from AdS/CFT
• A Covariant Holographic Entanglement Entropy Proposal
• Geometric and Renormalized Entropy in Conformal Field Theory
• Evolution of Entanglement Entropy in One-Dimensional Systems
• Quantum Extremal Surfaces: Holographic Entanglement Entropy beyond the Classical Regime
• Quantum corrections to holographic entanglement entropy
• The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole
• The Page curve of Hawking radiation from semiclassical geometry
• Entanglement and correlation functions following a local quench: a conformal field theory approach
• Structure of states which satisfy strong subadditivity of quantum entropy with equality
• Entanglement Tsunami: Universal Scaling in Holographic Thermalization
• Relative Entropy and Holography
• Time Dependence of Hawking Radiation Entropy
• Holographic Entanglement of Purification
• Holographic Mutual Information is Monogamous
• Holographic Evolution of Entanglement Entropy
• Quantum conditional mutual information and approximate Markov chains
• Entanglement hamiltonians in two-dimensional conformal field theory
• Holographic Local Quenches and Entanglement Density
• Universal terms for the entanglement entropy in 2+1 dimensions
• Remarks on the entanglement entropy for disconnected regions
• A Stereoscopic Look into the Bulk
• Inequalities for Quantum Entropy: A Review with Conditions for Equality
• Momentum-space entanglement and renormalization in quantum field theory
• Bit threads and holographic entanglement
• Spectral Geometry and One-loop Divergences on Manifolds with Conical Singularities
• Entanglement contour
• Information Flow in Black Hole Evaporation
• Geometric Aspects of Holographic Bit Threads
• Holographic entanglement contour, bit threads, and the entanglement tsunami
• Entanglement Entropy: A Perturbative Calculation
• Renyi generalizations of the conditional quantum mutual information
• Holographic Quantum Circuits from Splitting/Joining Local Quenches
• Shape Dependence of Entanglement Entropy in Conformal Field Theories
• Entanglement Entropy for Relevant and Geometric Perturbations
• Fine structure in holographic entanglement and entanglement contour
• Shape Dependence of Holographic Rényi Entropy in General Dimensions
• Holographic Inequalities and Entanglement of Purification
• A contour for the entanglement entropies in harmonic lattices
• Towards the generalized gravitational entropy for spacetimes with non-Lorentz invariant duals
• The negativity contour: a quasi-local measure of entanglement for mixed states
• Formulas for Partial Entanglement Entropy
• Entanglement contour and modular flow from subset entanglement entropies
• Conditional mutual information and self-commutator
• On the entanglement contour of excited states in the holographic CFT

Cited by in corpus (12)

• Balanced Partial Entanglement and Mixed State Correlations
• Entanglement entropy from entanglement contour: higher dimensions
• The PEE aspects of entanglement islands from bit threads
• Microcanonical Action and the Entropy of Hawking Radiation
• Covariant entanglement wedge cross-section, balanced partial entanglement and gravitational anomalies
• Ownerless island and partial entanglement entropy in island phases
• Quantum bit threads
• Geometrizing the Partial Entanglement Entropy: from PEE Threads to Bit Threads
• Ergotropy and entanglement in critical spin chains
• Weaving the (AdS) spaces with partial entanglement entropy threads
• Bulk reconstruction of AdS${}_{d+1}$ metrics and developing kinematic space
• Holographic Tensor Networks as Tessellations of Geometry