Holographic Entanglement of Purification from Conformal Field Theories

Abstract

We explore a conformal field theoretic interpretation of the holographic entanglement of purification, which is defined as the minimal area of entanglement wedge cross section. We argue that in AdS3/CFT2, the holographic entanglement of purification agrees with the entanglement entropy for a purified state, obtained from a special Weyl transformation, called path-integral optimizations. By definition, this special purified state has the minimal path-integral complexity. We confirm this claim in several examples.

arXiv comment7 pages, Revtex, 5 figures

References in corpus (45)

• The Large N Limit of Superconformal Field Theories and Supergravity
• Holographic Derivation of Entanglement Entropy from AdS/CFT
• Aspects of Holographic Entanglement Entropy
• A Covariant Holographic Entanglement Entropy Proposal
• Geometric and Renormalized Entropy in Conformal Field Theory
• Entanglement renormalization
• A class of quantum many-body states that can be efficiently simulated
• Complexity Equals Action
• Entanglement Renormalization and Holography
• Complexity and Shock Wave Geometries
• Maximin Surfaces, and the Strong Subadditivity of the Covariant Holographic Entanglement Entropy
• The Gravity Dual of a Density Matrix
• Causality & holographic entanglement entropy
• Tensor Network Renormalization
• Gravitational action with null boundaries
• Holographic Entanglement of Purification
• Liouville Action as Path-Integral Complexity: From Continuous Tensor Networks to AdS/CFT
• The entanglement of purification
• Anti-de Sitter Space from Optimization of Path Integrals in Conformal Field Theories
• Entanglement of purification: from spin chains to holography
• Surface/State Correspondence as a Generalized Holography
• Entanglement negativity and minimal entanglement wedge cross sections in holographic theories
• Bit threads and holographic entanglement
• Entanglement Wedge Cross Section from the Dual Density Matrix
• Search for narrow and broad dijet resonances in proton-proton collisions at $\sqrt{s}=$ 13 TeV and constraints on dark matter mediators and other new particles
• Einstein's Equations from Varying Complexity
• Path-Integral Complexity for Perturbed CFTs
• Tensor network renormalization yields the multi-scale entanglement renormalization ansatz
• Entanglement Wedge Reconstruction and Entanglement of Purification
• Geometric Aspects of Holographic Bit Threads
• Entanglement of Purification for Multipartite States and its Holographic Dual
• Holographic Spacetimes as Quantum Circuits of Path-Integrations
• Holographic Subregion Complexity from Kinematic Space
• Conditional and Multipartite Entanglements of Purification and Holography
• Holographic Inequalities and Entanglement of Purification
• Finding purifications with minimal entanglement
• Pulling the Boundary into the Bulk
• Entanglement of Purification in Free Scalar Field Theories
• Bulk locality and cooperative flows
• Holographic entanglement of purification for thermofield double states and thermal quench
• Entanglement of Purification and Multiboundary Wormhole Geometries
• Modular Flow as a Disentangler
• The holographic entropy zoo
• Gravity from entanglement for boundary subregions
• Minimal Purifications, Wormhole Geometries, and the Complexity=Action Proposal

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• Reflected Entropy and Entanglement Wedge Cross Section with the First Order Correction
• Generalizations of Reflected Entropy and the Holographic Dual
• Dynamics of Entanglement Wedge Cross Section from Conformal Field Theories
• Entanglement of Purification in Many Body Systems and Symmetry Breaking
• Quantum and Classical Correlations Inside the Entanglement Wedge
• Multipartite Reflected Entropy
• The connection between holographic entanglement and complexity of purification
• Notes on entanglement wedge cross sections
• Aspects of Hyperscaling Violating Geometries at Finite Cutoff
• Entanglement and Complexity of Purification in (1+1)-dimensional free Conformal Field Theories
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• Bit threads and holographic entanglement of purification
• Entanglement Wedges from Information Metric in Conformal Field Theories
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• Evolution of Entanglement Wedge Cross Section Following a Global Quench
• Geometry and Complexity of Path Integrals in Inhomogeneous CFTs
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• On the Role of Counterterms in Holographic Complexity
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• Holographic Coarse-Graining: Correlators from the Entanglement Wedge and Other Reduced Geometries
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• Inequalities of Holographic Entanglement of Purification from Bit Threads
• Entanglement of purification and disentanglement in CFTs
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• Bounding entanglement wedge cross sections
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• Optimized Correlation Measures in Holography
• Reflected multi-entropy and its holographic dual
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• Probing Phase Structure of Strongly Coupled Matter with Holographic Entanglement Measures
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• One-half reflected entropy is not a lower bound for entanglement of purification
• Holographic Complexity from the Crofton's Formula in Lorentzian AdS${}_3$
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• Covariant odd entanglement entropy in AdS${}_3$/CFT${}_2$
• Rényi Entanglement of Purification and Half Rényi Reflected Entropy in Free Scalar Theory
• A note on the kinematic space associated with a subregion