Some Aspects of Entanglement Wedge Cross-Section

Abstract

We consider the minimal area of the entanglement wedge cross section (EWCS) in Einstein gravity. In the context of holography, it is proposed that this quantity is dual to different information measures, e.g., entanglement of purification, logarithmic negativity and reflected entropy. Motivated by these proposals, we examine in detail the low and high temperature corrections to this quantity and show that it obeys the area law even in the finite temperature. We also study EWCS in nonrelativistic field theories with nontrivial Lifshitz and hyperscaling violating exponents. The resultant EWCS is an increasing function of the dynamical exponent due to the enhancement of spatial correlations between subregions for larger values of $z$. We find that EWCS is monotonically decreasing as the hyperscaling violating exponent increases. We also obtain this quantity for an entangling region with singular boundary in a three dimensional field theory and find a universal contribution where the coefficient depends on the central charge. Finally, we verify that for higher dimensional singular regions the corresponding EWCS obeys the area law.

arXiv comment31 pages, 10 figures, title changed, updated to match the published version

References in corpus (50)

• Holographic Derivation of Entanglement Entropy from AdS/CFT
• Aspects of Holographic Entanglement Entropy
• A Covariant Holographic Entanglement Entropy Proposal
• Complexity Equals Action
• Quantum corrections to holographic entanglement entropy
• Entanglement Renyi entropies in holographic theories
• Relative entropy equals bulk relative entropy
• Aspects of holography for theories with hyperscaling violation
• Holographic Entanglement of Purification
• Holographic Entanglement Entropy for General Higher Derivative Gravity
• The entanglement of purification
• Generalized entropy and higher derivative Gravity
• On Holographic Entanglement Entropy and Higher Curvature Gravity
• Entanglement of purification: from spin chains to holography
• Entanglement negativity and minimal entanglement wedge cross sections in holographic theories
• Universality of corner entanglement in conformal field theories
• AdS/CFT and Strong Subadditivity of Entanglement Entropy
• Gravity Dual of Quantum Information Metric
• Entanglement Wedge Cross Section from the Dual Density Matrix
• Charged Black Branes with Hyperscaling Violating Factor
• Strongly Coupled Gauge Theories: High and Low Temperature Behavior of Non-local Observables
• Complexity Growth with Lifshitz Scaling and Hyperscaling Violation
• Holographic Mutual Information at Finite Temperature
• Geometric Aspects of Holographic Bit Threads
• Entanglement Wedge Reconstruction and Entanglement of Purification
• Entanglement of Purification for Multipartite States and its Holographic Dual
• Holographic Entanglement of Purification from Conformal Field Theories
• Thermalization in backgrounds with hyperscaling violating factor
• Entanglement Entropy for Singular Surfaces
• Holographic Models for Theories with Hyperscaling Violation
• Conditional and Multipartite Entanglements of Purification and Holography
• Universal Thermal Corrections to Single Interval Entanglement Entropy for Conformal Field Theories
• Holographic Inequalities and Entanglement of Purification
• Corner contributions to holographic entanglement entropy in AdS4/BCFT3
• On the Time Evolution of Holographic n-partite Information
• Entanglement of Purification in Free Scalar Field Theories
• Towards Entanglement of Purification for Conformal Field Theories
• Entanglement of Purification in Many Body Systems and Symmetry Breaking
• Universal Thermal Corrections to Entanglement Entropy for Conformal Field Theories on Spheres
• Holographic entanglement of purification for thermofield double states and thermal quench
• Entanglement Evolution in Lifshitz-type Scalar Theories
• Entanglement of Purification and Multiboundary Wormhole Geometries
• Entanglement Entropy in Lifshitz Theories
• Monogamy, polygamy, and other properties of entanglement of purification
• Holographic Subregion Complexity for Singular Surfaces
• Entanglement Entropy for Singular Surfaces in Hyperscaling violating Theories
• Holographic Mutual Information for Singular Surfaces
• Entanglement of Purification in Holographic Systems
• Holographic Entanglement Entropy, Field Redefinition Invariance and Higher Derivative Gravity Theories
• Thermalization of Mutual Information in Hyperscaling Violating Backgrounds

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• Entanglement Wedge Cross Sections Require Tripartite Entanglement
• Entanglement Wedge Cross Section from CFT: Dynamics of Local Operator Quench
• Entanglement and Rényi Entropy of Multiple Intervals in $T\overline{T}$-Deformed CFT and Holography
• Balanced Partial Entanglement and the Entanglement Wedge Cross Section
• Reflected Entropy and Entanglement Wedge Cross Section with the First Order Correction
• Generalizations of Reflected Entropy and the Holographic Dual
• Quantum and Classical Correlations Inside the Entanglement Wedge
• Notes on entanglement wedge cross sections
• Aspects of Hyperscaling Violating Geometries at Finite Cutoff
• Bit threads and holographic entanglement of purification
• Balanced Partial Entanglement and Mixed State Correlations
• Entanglement negativity, reflected entropy, and anomalous gravitation
• Mixed state entanglement measures as probe for confinement
• Topological reflected entropy in Chern-Simons theories
• Islands for Entanglement Negativity
• Reflected entropy for free scalars
• Evolution of Entanglement Wedge Cross Section Following a Global Quench
• Long-distance entanglement of purification and reflected entropy in conformal field theory
• Holographic Mutual Information and Critical Exponents of the Strongly Coupled Plasma
• Covariant entanglement wedge cross-section, balanced partial entanglement and gravitational anomalies
• Holographic Study of Reflected Entropy in Anisotropic Theories
• Entanglement Wedge Cross Section in Holographic Excited States
• CFT sewing as the dual of AdS cut-and-paste
• Holographic study of entanglement and complexity for mixed states
• Effect of back reaction on entanglement and subregion volume complexity in strongly coupled plasma
• A Field Theory Study of Entanglement Wedge Cross Section: Odd Entropy
• Informational properties for Einstein-Maxwell-Dilaton Gravity
• Informational properties of holographic Lifshitz field theory
• Holographic Entanglement of Purification near a Critical Point
• Entanglement measures for non-conformal D-branes
• Entanglement wedge cross-section in shock wave geometries
• Temperature Dependence of Entanglement of Purification in Presence of Chemical Potential
• Inequalities of Holographic Entanglement of Purification from Bit Threads
• Entanglement Wedge Minimum Cross-section in Holographic Massive Gravity Theory
• Entanglement wedge cross section for noncommutative Yang-Mills theory
• Entanglement Wedge Cross Section Growth During Thermalization
• Quantum information probes of charge fractionalization in large-$N$ gauge theories
• Covariant holographic negativity from the entanglement wedge in AdS${}_3/$CFT${}_2$
• Reflected entropy in Galilean conformal field theories and flat holography
• Bounding entanglement wedge cross sections
• Entanglement Wedge Cross Section with Gauss-Bonnet Corrections and Thermal Quench
• Odd entanglement entropy in $\text{T}\bar{\text{T}}$ deformed CFT${}_2$s and holography
• Multipartite Optimized Correlation Measures and Holography
• Optimized Correlation Measures in Holography
• The mixed-state entanglement in holographic p-wave superconductor model
• Improved proof-by-contraction method and relative homologous entropy inequalities
• Probing Phase Structure of Strongly Coupled Matter with Holographic Entanglement Measures
• Mixed state entanglement in deformed field theory at finite temperature
• Non-Conformal Behavior of Holographic Entanglement Measures
• Information theoretic measures for Lifshitz system
• More on entanglement properties of $Li{f}_4^{(2)}\times S^1\times S^5$ spacetime with string excitations
• One-half reflected entropy is not a lower bound for entanglement of purification
• Phase Transitions of Correlations in Black Hole Geometries
• Entanglement wedge cross section inequalities in AdS/BCFT
• A holographic realization of correlation and mutual information
• Entropy of Hawking Radiation for Two-Sided Hyperscaling Violating Black Branes
• Coarse-Grained Fixed-Point Tensor Networks and Holographic Reflected Entropy in 3D Gravity
• Rényi Entanglement of Purification and Half Rényi Reflected Entropy in Free Scalar Theory