Holographic Entanglement of Purification

Abstract

We study properties of the minimal cross section of entanglement wedge which connects two disconnected subsystems in holography. In particular we focus on various inequalities which are satisfied by this quantity. They suggest that it is a holographic counterpart of the quantity called entanglement of purification, which measures a bipartite correlation in a given mixed state. We give a heuristic argument which supports this identification based on a tensor network interpretation of holography. This implies that the entanglement of purification satisfies the strong superadditivity for holographic conformal field theories.

Revtex, 6 pages + appendices. v2: comments and references added, minor corrections

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Cited by in corpus (237)

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• Beyond Toy Models: Distilling Tensor Networks in Full AdS/CFT
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• Exponential Thermal Tensor Network Approach for Quantum Lattice Models
• Geometric Aspects of Holographic Bit Threads
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• Reflected Entropy for an Evaporating Black Hole
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• Holographic entanglement contour, bit threads, and the entanglement tsunami
• Quantum Information in Holographic Duality
• Holographic Subregion Complexity from Kinematic Space
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• Conditional and Multipartite Entanglements of Purification and Holography
• Some Aspects of Entanglement Wedge Cross-Section
• Correlation measures and the entanglement wedge cross-section after quantum quenches in two-dimensional conformal field theories
• Universal tripartite entanglement in one-dimensional many-body systems
• Bit Threads and Holographic Monogamy
• Bit threads and holographic entanglement of purification
• Holographic entanglement negativity and replica symmetry breaking
• Finding purifications with minimal entanglement
• Towards Bulk Metric Reconstruction from Extremal Area Variations
• Balanced Partial Entanglement and the Entanglement Wedge Cross Section
• Reflected Entropy and Entanglement Wedge Cross Section with the First Order Correction
• Defect Extremal Surface for Reflected Entropy
• Reflected entropy in random tensor networks
• Quantum vs. classical information: operator negativity as a probe of scrambling
• Pulling the Boundary into the Bulk
• Entanglement of Purification in Free Scalar Field Theories
• Generalizations of Reflected Entropy and the Holographic Dual
• Entanglement of Purification in Many Body Systems and Symmetry Breaking
• Dynamics of Entanglement Wedge Cross Section from Conformal Field Theories
• Multipartite Reflected Entropy
• The connection between holographic entanglement and complexity of purification
• Quantum and Classical Correlations Inside the Entanglement Wedge
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• The correlation function of (1,1) and (2,2) supersymmetric theories with $T\bar{T}$ deformation
• Entanglement Wedge in Flat Holography and Entanglement Negativity
• Bulk locality and cooperative flows
• Is entanglement a probe of confinement?
• Holographic entanglement of purification for thermofield double states and thermal quench
• Reflected entropy, symmetries and free fermions
• Reflected Entropy in Double Holography
• $T\bar{T}$, the entanglement wedge cross section, and the breakdown of the split property
• Entanglement of Purification and Multiboundary Wormhole Geometries
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• Aspects of Hyperscaling Violating Geometries at Finite Cutoff
• Entanglement Wedges from Information Metric in Conformal Field Theories
• Balanced Partial Entanglement and Mixed State Correlations
• Bit threads and holographic entanglement of purification
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• Hawking Radiation Correlations of Evaporating Black Holes in JT Gravity
• Topological reflected entropy in Chern-Simons theories
• Mixed state entanglement measures as probe for confinement
• Modular Flow as a Disentangler
• Decoherence in Conformal Field Theory
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• Islands for Entanglement Negativity
• Reflected entropy for free scalars
• Complexity of mixed Gaussian states from Fisher information geometry
• Page Curve for Entanglement Negativity through Geometric Evaporation
• Entanglement of Local Operators and the Butterfly Effect
• Surface/State correspondence and $T\overline{T}$ deformation
• Covariant bit threads
• The role of mutual information in the Page curve
• Gravity Dual of Connes Cocycle Flow
• Holographic Purification Complexity
• Towards precision holography
• Toward random tensor networks and holographic codes in CFT
• Local measures of entanglement in black holes and CFTs
• Evolution of Entanglement Wedge Cross Section Following a Global Quench
• The Markov gap in the presence of islands
• Correlation measures and distillable entanglement in AdS/CFT
• On de Sitter future-past extremal surfaces and the "entanglement wedge"
• The Quantum Entropy Cone of Hypergraphs
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• Barrier from chaos: operator entanglement dynamics of the reduced density matrix
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• Bit thread, entanglement distillation, and entanglement of purification
• Long-distance entanglement of purification and reflected entropy in conformal field theory
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• Coarse-Graining Holographic States: A Semiclassical Flow in General Spacetimes
• Deriving the PEE proposal from the Locking bit thread configuration
• On the Role of Counterterms in Holographic Complexity
• Covariant entanglement wedge cross-section, balanced partial entanglement and gravitational anomalies
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• Evolutions of entanglement and complexity after a thermal quench in massive gravity theory
• Ownerless island and partial entanglement entropy in island phases
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• Holographic reconstruction of black hole spacetime: machine learning and entanglement entropy
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• Entanglement Wedge Cross Section in Holographic Excited States
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• CFT sewing as the dual of AdS cut-and-paste
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• Reflected Entropy for Communicating Black Holes I: Karch-Randall Braneworlds
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• Holographic Coarse-Graining: Correlators from the Entanglement Wedge and Other Reduced Geometries
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• Entanglement Wedge Cross Section Growth During Thermalization
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• Reflected Entropy and Entanglement Negativity for Holographic Moving Mirrors
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• Universal entanglement signatures of interface conformal field theories
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• Covariant holographic negativity from the entanglement wedge in AdS${}_3/$CFT${}_2$
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• Bounding entanglement wedge cross sections
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• Correlations of mixed systems in confining backgrounds
• Towards an Entanglement Measure for Mixed States in CFTs Based on Relative Entropy
• Entanglement Wedge Cross Section Inequalities from Replicated Geometries
• Properties of the contraction map for holographic entanglement entropy inequalities
• On minimal entanglement wedge cross section for holographic entanglement negativity
• More on the upper bound of holographic n-partite information
• An alternative to purification in CFT
• Entanglement Wedge Minimum Cross-Section for Holographic Aether Gravity
• Holographic relations for OPE blocks in excited states
• Bulk private curves require large conditional mutual information
• Entanglement Wedge Cross Section with Gauss-Bonnet Corrections and Thermal Quench
• The Reflected Entanglement Spectrum for Free Fermions
• Mixed-state Entanglement for AdS Born-Infeld Theory
• Reconstructing black hole exteriors and interiors using entanglement and complexity
• Multipartite entanglement and topology in holography
• Odd entanglement entropy in $\text{T}\bar{\text{T}}$ deformed CFT${}_2$s and holography
• A geodesic Witten diagram description of holographic entanglement entropy and its quantum corrections
• Pseudo entropy and pseudo-Hermiticity in quantum field theories
• Holographic Reflected Entropy and Islands in Interface CFTs
• Holographic thermal entropy from geodesic bit threads
• Wormholes and holographic decoherence
• Optimized Correlation Measures in Holography
• The entanglement properties of holographic QCD model with a critical end point
• The mixed-state entanglement in holographic p-wave superconductor model
• Multipartite Optimized Correlation Measures and Holography
• Improved proof-by-contraction method and relative homologous entropy inequalities
• Reflected multi-entropy and its holographic dual
• Mixed state information theoretic measures in boosted black brane
• Entanglement Negativity and Replica Symmetry Breaking in General Holographic States
• Mixed state entanglement in deformed field theory at finite temperature
• Bit threads on hypergraphs
• Odd entanglement entropy in Galilean conformal field theories and flat holography
• A quantum information perspective on meson melting
• Musings on SVD and pseudo entanglement entropies
• Bridging Boundaries: $T\bar{T}$, Double Holography, and Reflected Entropy
• Probing Phase Structure of Strongly Coupled Matter with Holographic Entanglement Measures
• Holographic entanglement properties in the QCD phase diagram from EMD models
• Non-Conformal Behavior of Holographic Entanglement Measures
• Entanglement Negativity and Defect Extremal Surface
• Operational symmetries of entangled states
• Counting atypical black hole microstates from entanglement wedges
• Holographic entanglement entropy and complexity for the cosmological braneworld model
• Critical distance and Crofton form in confining geometries
• One-half reflected entropy is not a lower bound for entanglement of purification
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• Covariant holographic reflected entropy in $Ad{S}_3/CF{T}_2$
• Information theoretic measures for Lifshitz system
• The Markov gap for geometric reflected entropy
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• Insensitivity of the complexity rate of change to the conformal anomaly and Lloyd's bound as a possible renormalization condition
• Squashed Entanglement from Generalized Rindler Wedge
• Shrinking of Operators in Quantum Error Correction and AdS/CFT
• Does connected wedge imply distillable entanglement?
• Holographic multipartite entanglement structures in IR modified geometries
• Entanglement wedge cross section inequalities in AdS/BCFT
• Phase Transitions of Correlations in Black Hole Geometries
• Entanglement Negativity in Flat Holography
• Quantum correlation in quark-gluon medium
• Entangled universes
• Holographic entanglement negativity for a single subsystem in conformal field theories with a conserved charge
• Position and momentum operators for a moving particle in bulk
• Complexity of Magnetization and Magnetic Simplification
• Long-range correlation of CMB temperature fluctuations from the holographic entanglement entropy
• Geometry of Entanglement
• Investigating the role of mutual information in the Page curve for a functional renormalization group improved Schwarzschild black hole
• Covariant odd entanglement entropy in AdS${}_3$/CFT${}_2$
• Renyi reflected entropy and entanglement wedge cross section with cosmic branes in AdS/BCFT
• How Einstein's Equation Emerges From CFT${}_2$
• Upper bound of holographic entanglement entropy combinations
• Markov Gap and Bound Entanglement in Haar Random State
• Coarse-Grained Fixed-Point Tensor Networks and Holographic Reflected Entropy in 3D Gravity
• Generalized Entanglement of Purification Criteria for 2-Producible States in Multipartite Systems
• Generalised Entanglement Entropies from Unit-Invariant Singular Value Decomposition
• Entanglement Entropy and Complexity of Multicomponent Universe from Holography
• Spectral Projections for Density Matrices in Quantum Field Theories
• String Scattering and Evolution of Ryu-Takayanagi Surface
• A note on the kinematic space associated with a subregion
• Quantum Information Approaches to Quantum Gravity
• Non-perturbative Aspects of Quantum Field Theories from Holography
• Odd Entanglement Entropy and Logarithmic Negativity for Thermofield Double States
• Rényi Entanglement of Purification and Half Rényi Reflected Entropy in Free Scalar Theory
• Correlations in geometric states
• Holographic Reflected Entropy: Islands and Defect Phases
• Holographic Entanglement Distillation from the Surface State Correspondence