Relative entropy equals bulk relative entropy

Abstract

We consider the gravity dual of the modular Hamiltonian associated to a general subregion of a boundary theory. We use it to argue that the relative entropy of nearby states is given by the relative entropy in the bulk, to leading order in the bulk gravitational coupling. We also argue that the boundary modular flow is dual to the bulk modular flow in the entanglement wedge, with implications for entanglement wedge reconstruction.

23 pages, 3 figures

References in corpus (12)

• Towards a derivation of holographic entanglement entropy
• Holographic representation of local bulk operators
• Causality & holographic entanglement entropy
• Relative entropy and the Bekenstein bound
• Universality of Gravity from Entanglement
• Tomography from Entanglement
• The entanglement of distillation for gauge theories
• A proof of the generalized second law for rapidly-evolving Rindler horizons
• Area terms in entanglement entropy
• Renyi entropy, stationarity, and entanglement of the conformal scalar
• Inviolable energy conditions from entanglement inequalities
• The Gravity Duals of Modular Hamiltonians

Cited by in corpus (335)

• Replica Wormholes and the Entropy of Hawking Radiation
• The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole
• The entropy of Hawking radiation
• Measuring out-of-time-order correlations and multiple quantum spectra in a trapped ion quantum magnet
• Reconstruction of Bulk Operators within the Entanglement Wedge in Gauge-Gravity Duality
• The Ryu-Takayanagi Formula from Quantum Error Correction
• The Gravity Dual of Renyi Entropy
• Deriving covariant holographic entanglement
• Entanglement islands in higher dimensions
• Modular Hamiltonians for Deformed Half-Spaces and the Averaged Null Energy Condition
• Bulk locality from modular flow
• Information radiation in BCFT models of black holes
• Gravity and the Crossed Product
• Inconsistency of Islands in Theories with Long-Range Gravity
• Entanglement of purification: from spin chains to holography
• Entanglement negativity and minimal entanglement wedge cross sections in holographic theories
• Covariant phase space with boundaries
• Flat entanglement spectra in fixed-area states of quantum gravity
• Local phase space and edge modes for diffeomorphism-invariant theories
• Gravity/Ensemble Duality
• Modular Hamiltonians on the null plane and the Markov property of the vacuum state
• Entropy, Extremality, Euclidean Variations, and the Equations of Motion
• Entanglement Wedge Reconstruction via Universal Recovery Channels
• Low-dimensional de Sitter quantum gravity
• On Volumes of Subregions in Holography and Complexity
• Quantum de Sitter horizon entropy from quasicanonical bulk, edge, sphere and topological string partition functions
• A General Proof of the Quantum Null Energy Condition
• Black holes, complexity and quantum chaos
• Decoding the Apparent Horizon: A Coarse-Grained Holographic Entropy
• Holographic Complexity in Vaidya Spacetimes I
• Quantum Extremal Islands Made Easy, PartIII: Complexity on the Brane
• Simple holographic models of black hole evaporation
• Entanglement Phase Structure of a Holographic BCFT in a Black Hole Background
• Complexity of Mixed States in QFT and Holography
• $T\bar{T}$ and EE, with implications for (A)dS subregion encodings
• Generalized entropy for general subregions in quantum gravity
• Defects in Jackiw-Teitelboim Quantum Gravity
• Complexity and the bulk volume, a new York time story
• Beyond Toy Models: Distilling Tensor Networks in Full AdS/CFT
• Information Flow in Black Hole Evaporation
• Expanding the Black Hole Interior: Partially Entangled Thermal States in SYK
• Entanglement Wedge Reconstruction and Entanglement of Purification
• Pulling Out the Island with Modular Flow
• Coarse Graining Holographic Black Holes
• Entropy and modular Hamiltonian for a free chiral scalar in two intervals
• Learning the Alpha-bits of Black Holes
• Entanglement entropy and superselection sectors I. Global symmetries
• Quantum Information in Holographic Duality
• A modular toolkit for bulk reconstruction
• Gravitational Thermodynamics of Causal Diamonds in (A)dS
• The boundary dual of the bulk symplectic form
• Pure de Sitter space and the island moving back in time
• Symmetry resolved relative entropies and distances in conformal field theory
• Effective entropy of quantum fields coupled with gravity
• Loop Quantum Gravity, Exact Holographic Mapping, and Holographic Entanglement Entropy
• Some Aspects of Entanglement Wedge Cross-Section
• Cauchy Slice Holography: A New AdS/CFT Dictionary
• Entanglement Hamiltonians of lattice models via the Bisognano-Wichmann theorem
• Relative entropy of excited states in two dimensional conformal field theories
• Quantum minimal surfaces from quantum error correction
• Fine structure in holographic entanglement and entanglement contour
• Modular Hamiltonians of excited states, OPE blocks and emergent bulk fields
• Relative entropy and the RG flow
• A New Proposal for Holographic BCFT
• Holographic entanglement negativity and replica symmetry breaking
• Superdensity Operators for Spacetime Quantum Mechanics
• Spacetime Fluctuations in AdS/CFT
• Symmetry decomposition of relative entropies in conformal field theory
• Large Breakdowns of Entanglement Wedge Reconstruction
• Signatures of global symmetry violation in relative entropies and replica wormholes
• On New Proposal for Holographic BCFT
• A CFT Perspective on Gravitational Dressing and Bulk Locality
• Entanglement hamiltonians in 1D free lattice models after a global quantum quench
• Jackiw-Teitelboim Gravity from the Karch-Randall Braneworld
• Sewing spacetime with Lorentzian threads: complexity and the emergence of time in quantum gravity
• Local bulk physics from intersecting modular Hamiltonians
• Entanglement Wedge Reconstruction using the Petz Map
• Quantum Gravity in the Lab: Teleportation by Size and Traversable Wormholes, Part II
• Edge modes as reference frames and boundary actions from post-selection
• Linearity of Holographic Entanglement Entropy
• The entanglement spectrum of chiral fermions on the torus
• Exploring the Tensor Networks/AdS Correspondence
• Classifying boundary conditions in JT gravity: from energy-branes to $\alpha$-branes
• Modular Berry Connection
• A proposal for 3d quantum gravity and its bulk factorization
• Subsystem Trace Distance in Quantum Field Theory
• Quantum vs. classical information: operator negativity as a probe of scrambling
• Reflected entropy in random tensor networks
• Connecting Fisher information to bulk entanglement in holography
• Pulling the Boundary into the Bulk
• Island for Gravitationally Prepared State and Pseudo Entanglement Wedge
• Relative entropy of excited states in conformal field theories of arbitrary dimensions
• Aspects of AdS${}_2$ Quantum Gravity and the Karch-Randall Braneworld
• A Holographic Proof of Rényi Entropic Inequalities
• Thermal out-of-time-order correlators, KMS relations, and spectral functions
• Probing phase transitions of holographic entanglement entropy with fixed area states
• Entanglement Wedges for Gravitating Regions
• Holographic spacetime, black holes and quantum error correcting codes: A review
• Microcanonical Path Integrals and the Holography of small Black Hole Interiors
• A Modular Sewing Kit for Entanglement Wedges
• Holographic Order from Modular Chaos
• Finding Pythons in Unexpected Places
• One-loop universality of holographic codes
• Energy is Entanglement
• Towards Black Hole Evaporation in Jackiw-Teitelboim Gravity
• Crossed product algebras and generalized entropy for subregions
• Entanglement Wedge Reconstruction and the Information Paradox
• Spacetime from Unentanglement
• On the Holographic Dual of a Topological Symmetry Operator
• Local Modular Hamiltonians from the Quantum Null Energy Condition
• Entanglement Entropy of Two Coupled SYK Models and Eternal Traversable Wormhole
• Relative Entanglement Entropies in 1+1-dimensional conformal field theories
• Modular Hamiltonians for the massless Dirac field in the presence of a defect
• The Holographic Shape of Entanglement and Einstein's Equations
• Entanglement Wedges from Information Metric in Conformal Field Theories
• Multipartite Purification, Multiboundary Wormholes and Islands in AdS${}_3$/CFT${}_2$
• Modular Flow of Excited States
• Genus Two Partition Functions and Renyi Entropies of Large c CFTs
• Ensemble from Coarse Graining: Reconstructing the Interior of an Evaporating Black Hole
• Quantum Null Energy Condition and its (non)saturation in 2d CFTs
• Modular Flow as a Disentangler
• Distinguishing Random and Black Hole Microstates
• Bulk entanglement entropy in perturbative excited states
• Inside Out: Meet The Operators Inside The Horizon
• Generalized entanglement entropies in two-dimensional conformal field theory
• Bulk metric reconstruction from boundary entanglement
• Entanglement and relative entropies for low-lying excited states in inhomogeneous one-dimensional quantum systems
• Relative entropy for coherent states from Araki formula
• Near-optimal covariant quantum error-correcting codes from random unitaries with symmetries
• Covariant bit threads
• Modular Hamiltonians in flat holography and (W)AdS/WCFT
• Subsystem trace distance in low-lying states of $(1+1)$-dimensional conformal field theories
• Cutoff Dependence and Complexity of the CFT${}_2$ Ground State
• Islands with Gravitating Baths: Towards ER = EPR
• From entanglement generated dynamics to the gravitational anomaly and chiral central charge
• Gravity Dual of Connes Cocycle Flow
• Holographic scattering requires a connected entanglement wedge
• TASI Lectures on the Emergence of the Bulk in AdS/CFT
• Gauge Invariant Target Space Entanglement in D-Brane Holography
• Bag-of-gold spacetimes, Euclidean wormholes, and inflation from domain walls in AdS/CFT
• The Quantum Null Energy Condition, Entanglement Wedge Nesting, and Quantum Focusing
• Quantum information measures for restricted sets of observables
• Comments on black hole interiors and modular inclusions
• Towards classification of holographic multi-partite entanglement measures
• Symmetries, charges and conservation laws at causal diamonds in general relativity
• On the interior geometry of a typical black hole microstate
• Holographic cameras: an eye for the bulk
• Complexity and entanglement in non-local computation and holography
• On de Sitter future-past extremal surfaces and the "entanglement wedge"
• Equivalence of Emergent de Sitter Spaces from Conformal Field Theory
• Bulk Entanglement Entropy and Matrices
• Complexity/Action duality of shock wave geometry in a massive gravity theory
• No Simple Dual to the Causal Holographic Information?
• Modular Commutators in Conformal Field Theory
• Local quenches, bulk entanglement entropy and a unitary Page curve
• Equivalent Equations of Motion for Gravity and Entropy
• Relative entropy for coherent states in chiral CFT
• Probing typical black hole microstates
• Entanglement Entropy and Subregion Complexity in Thermal Perturbations around Pure-AdS Spacetime
• Approximate Bacon-Shor Code and Holography
• Coarse-Graining Holographic States: A Semiclassical Flow in General Spacetimes
• Bulk Locality in AdS/CFT Correspondence
• The Entanglement Wedge of Unknown Couplings
• Quantum Null Geometry and Gravity
• One-shot holography
• Looking at Shadows of Entanglement Wedges
• The holographic entropy cone from marginal independence
• A Bound on Holographic Entanglement Entropy from Inverse Mean Curvature Flow
• Comments on Defining Entanglement Entropy
• Precursors, Gauge Invariance, and Quantum Error Correction in AdS/CFT
• The holographic map as a conditional expectation
• Modular Hamiltonian for (holographic) excited states
• The holographic entropy zoo
• Entanglement entropy of linearized gravitons in a sphere
• Building Tensor Networks for Holographic States
• Holographic quantum tasks with input and output regions
• Emergence of spacetime from the algebra of total modular Hamiltonians
• Holographic Relative Entropy in Infinite-dimensional Hilbert Spaces
• Bulk entanglement entropy for photons and gravitons in AdS${}_3$
• A Survey of Black Hole Thermodynamics
• Quantum tasks require islands on the brane
• Black Hole Scattering and Partition Functions
• Observer-dependent black hole interior from operator collision
• Grey-body Factors, Irreversibility and Multiple Island Saddles
• Entanglement Wedge Reconstruction of Infinite-dimensional von Neumann Algebras using Tensor Networks
• The connected wedge theorem and its consequences
• Quantum tasks in holography
• Bulk reconstruction using timelike entanglement in (A)dS
• Symmetry-resolved modular correlation functions in free fermionic theories
• Complete Einstein equation from the generalized First Law of Entanglement
• State-Dependent Divergences in the Entanglement Entropy
• Ryu-Takayanagi Area as an Entanglement Edge Term
• Bootstrapping Quantum Extremal Surfaces I: The Area Operator
• Berry phases, wormholes and factorization in AdS/CFT
• Rindler Bulk Reconstruction and Subregion Duality in AdS/CFT
• The Boundary Dual of Bulk Local Operators
• Black Hole and de Sitter Microstructures from a Semiclassical Perspective
• Superselection Sectors of Gravitational Subregions
• News vs Information
• Bulk Reconstruction Beyond the Entanglement Wedge
• A Type $I$ Approximation of the Crossed Product
• Explicit reconstruction of the entanglement wedge
• Entanglement island, miracle operators and the firewall
• Seeing the Entanglement Wedge
• Holographic Coarse-Graining: Correlators from the Entanglement Wedge and Other Reduced Geometries
• Bulk reconstruction for spinor fields in AdS/CFT
• Entanglement wedge reconstruction and correlation measures in mixed states: modular flows versus quantum recovery channels
• The Holographic Dual of the Entanglement Wedge Symplectic Form
• Surface growth scheme for bulk reconstruction and tensor network
• Resolving modular flow: a toolkit for free fermions
• A First Law of Entanglement Rates from Holography
• Modular Hamiltonian of the scalar field in the semi infinite line: dimensional reduction for spherically symmetric regions
• Entropy for spherically symmetric, dynamical black holes from the relative entropy between coherent states of a scalar quantum field
• Quantum bit threads and holographic entanglement
• Quantum Error Correction from Complexity in Brownian SYK
• Geometrical tools for embedding fields, submanifolds, and foliations
• Marginal quenches and drives in Tomonaga-Luttinger liquids
• Scattering strings off quantum extremal surfaces
• Bridging two quantum quench problems -- local joining quantum quench and Möbius quench -- and their holographic dual descriptions
• Hartle-Hawking state and its factorization in 3d gravity
• Holography and unitarity
• Nonlocal multi-trace sources and bulk entanglement in holographic conformal field theories
• Covariant holographic negativity from the entanglement wedge in AdS${}_3/$CFT${}_2$
• Classical Spacetimes as Amplified Information in Holographic Quantum Theories
• Python's Lunches in Jackiw-Teitelboim gravity with matter
• Holographic baby universes: an observable story
• The action of HRT-areas as operators in semiclassical gravity
• Rényi entropies and area operator from gravity with Hayward term
• Trace distance between fermionic Gaussian states from a truncation method
• Non-Isometric Quantum Error Correction in Gravity
• Modular Hamiltonian for de Sitter diamonds
• Emergent Gravity in a Holographic Universe
• Entanglement Entropy in Jackiw-Teitelboim Gravity
• Perturbative quantum evolution of the gravitational state and dressing in general backgrounds
• Chaos and relative entropy
• The holographic dual of Rényi relative entropy
• Modular Hamiltonians and large diffeomorphisms in $Ad{S}_3$
• On minimal entanglement wedge cross section for holographic entanglement negativity
• Operational islands and black hole dissipation in JT gravity
• Entanglement Entropy and Modular Hamiltonian of free fermion with deformations on a torus
• Holographic equivalence between the first law of entanglement entropy and the linearized gravitational equations
• Quantum Error Correction and Holographic Information from Bilocal Holography
• Meson content of entanglement spectra after integrable and nonintegrable quantum quenches
• Bulk private curves require large conditional mutual information
• Thermal states are vital: Entanglement Wedge Reconstruction from Operator-Pushing
• Quantum Entanglement on Black Hole Horizons in String Theory and Holography
• Exploring causality in braneworld/cutoff holography via holographic scattering
• Entanglement Entropy in Internal Spaces and Ryu-Takayanagi Surfaces
• Numerical calculations on the relative entanglement entropy in critical spin chains
• Marginally Trapped Surfaces and AdS/CFT
• Note on surface growth approach for bulk reconstruction
• Renyi divergences from Euclidean quenches
• Topological string entanglement
• Negative Complexity of Formation: the Compact Dimensions Strike Back
• Black Hole Information Recovery in JT Gravity
• Petz map and Python's lunch
• Explicit reconstruction of the entanglement wedge via the Petz map
• Modular parallel transport of multiple intervals in 1+1-dimensional free fermion theory
• Properties of Modular Hamiltonians on Entanglement Plateaux
• Horizon thermodynamics and cosmological equations: A holographic-like connection between thermostatistical quantities on a cosmological horizon and in the bulk
• Finite Entanglement Entropy in String Theory
• Entanglement Entropy and Duality
• Gravity from Entanglement and RG Flow in a Top-down Approach
• Operator Size for Holographic Field Theories
• Pacman geometries and the Hayward term in JT gravity
• Quantum Area Fluctuations from Gravitational Phase Space
• Nonperturbative gravity corrections to bulk reconstruction
• Recovering Infalling Information via String Spreading
• Large and Small Corrections to the JLMS Formula from Replica Wormholes
• Modular Hamiltonians for Euclidean Path Integral States
• Duality of Ryu-Takayanagi surfaces inside and outside the horizon
• Spectrum of Modular Hamiltonian in the Vacuum and Excited States
• Precursor problem and holographic mutual information
• The Algebraic Structure Underlying Pole-Skipping Points
• On the first law of entanglement for Quasi-Topological gravity
• Holographic moving mirrors
• Bulk Matter and the Boundary Quantum Null Energy Condition
• Dressing bulk fields in AdS${}_3$
• The Holographic Map of an Evaporating Black Hole
• Towards bit threads in general gravitational spacetimes
• Causal Density Matrices
• Measuring the Black Hole Interior from the Exterior
• The area operator and fixed area states in conformal field theories
• Correlation function of modular Hamiltonians
• First Law and Quantum Correction for Holographic Entanglement Contour
• Holographic Bulk Reconstruction And Cosmological Singularities
• Reconstructing bulk equation of motion using CFT modular Hamiltonians
• Reconstruction wedges in $AdS/CFT$ with boundary fractallike structures
• On Quantum Information Before the Page Time
• Entanglement in conformal field theory and holography
• Relational bulk reconstruction from modular flow
• Holographic thermodynamic relation for dissipative and non-dissipative universes in a flat FLRW cosmology
• Holographic geometry/real-space entanglement correspondence and metric reconstruction
• Entanglement Entropy with a Time-dependent Hamiltonian
• The Markov gap for geometric reflected entropy
• Quantum many-body physics from a gravitational lens
• Holography from Decoherence and Entanglement
• Relative Entropy and Torsion Coupling
• Black hole interior Petz map reconstruction and Papadodimas-Raju proposal
• Subregion duality, wedge classification and no global symmetries in AdS/CFT
• Boundary and bulk notions of transport in the AdS${}_3$/CFT${}_2$ correspondence
• Thesis: Tensor networks for dynamic spacetimes
• Extremality as a Consistency Condition on Subregion Duality
• Realize Emergent Gravity to Generic Situations
• Correlation function with the insertion of zero modes of modular Hamiltonians
• Nearly AdS${}_2$ holography in quantum CGHS model
• Simple Bulk Reconstruction in AdS/CFT Correspondence
• The Parts of the Gravitational Field
• The Ryu-Takayanagi Formula from Quantum Error Correction: An Algebraic Treatment of the Boundary CFT
• Shrinking of Operators in Quantum Error Correction and AdS/CFT
• Holographic phenomenology via overlapping degrees of freedom
• Virasoro algebras, kinematic space and the spectrum of modular Hamiltonians in CFT${}_2$
• Geometric Surprises in the Python's Lunch Conjecture
• Revisiting holographic codes with fractal-like boundary erasures
• Entangled universes
• Estimating time in quantum chaotic systems and black holes
• Monotonicity of RG flow in emergent dual holography of worldsheet nonlinear $\sigma$ model
• Caustics bounding entanglement wedges
• Modave Lectures on Quantum Information: An Introduction to Channels and Applications to Black Holes and AdS/CFT
• Purification Complexity without Purifications
• Aspects of Entanglement Entropy in Algebraic Quantum Field Theory
• Causal shadow and non-local modular flow: from degeneracy to perturbative genesis by correlation
• Growth of a renormalized operator as a probe of chaos
• Violation of Unitarity in Gravitational Subregions
• Area law and OPE blocks in CFT
• Probing the Factorized Island Branch with the Capacity of Entanglement in JT Gravity
• A note on the kinematic space associated with a subregion
• Entanglement in descendants
• Subsystem fidelity in two-dimensional conformal field theories
• Fluctuations and non-Gaussianity in de Sitter spacetime from holographic entanglement entropy
• The generalized first law for more general matter
• Searching for emergent spacetime in spin glasses
• Dressing bulk spinor fields in AdS${}_3$
• Holographic Tensor Networks as Tessellations of Geometry
• Quantum Information Approaches to Quantum Gravity