Entanglement negativity, reflected entropy, and anomalous gravitation

Abstract

We investigate mixed state entanglement measures of entanglement negativity and reflected entropy for bipartite states in two dimensional conformal field theories with an anomaly through appropriate replica techniques. Furthermore we propose holographic constructions for these measures from the corresponding bulk dual geometries involving topologically massive gravity in AdS${}_3$ and find exact agreement with the field theory results. In this connection we extend an earlier holographic proposal for the entanglement negativity to the bulk action with a gravitational Chern-Simons term and compute its contribution to the entanglement wedge cross section dual to the reflected entropy.

arXiv comment49 pages, 14 figures and 1 appendix,v2: minor modifications, references added, v3: matches the published version, v4: erratum included

References in corpus (56)

• Separability Criterion for Density Matrices
• A computable measure of entanglement
• Holographic Derivation of Entanglement Entropy from AdS/CFT
• The World as a Hologram
• Separability of Mixed States: Necessary and Sufficient Conditions
• Entanglement Entropy and Quantum Field Theory
• A Covariant Holographic Entanglement Entropy Proposal
• Entanglement entropy and conformal field theory
• The logarithmic negativity: A full entanglement monotone that is not convex
• Towards a derivation of holographic entanglement entropy
• Generalized gravitational entropy
• Entanglement Renyi entropies in holographic theories
• Entanglement negativity in quantum field theory
• Universality of Long-Distance AdS Physics from the CFT Bootstrap
• Entanglement entropy of two disjoint intervals in conformal field theory
• Holographic Entanglement of Purification
• Entanglement negativity in extended systems: A field theoretical approach
• Deriving covariant holographic entanglement
• Holographic Gravitational Anomalies
• Holographic Calculations of Renyi Entropy
• Proof of the Holographic Formula for Entanglement Entropy
• Entanglement entropy in Galilean conformal field theories and flat holography
• Entanglement of purification: from spin chains to holography
• Entanglement negativity and minimal entanglement wedge cross sections in holographic theories
• Finite temperature entanglement negativity in conformal field theory
• Wilson Lines and Entanglement Entropy in Higher Spin Gravity
• Semi-classical central charge in topologically massive gravity
• Black Hole Entropy in the presence of Chern-Simons Terms
• Derivation of holographic negativity in AdS${}_3$/CFT${}_2$
• Islands for Reflected Entropy
• Comments on Entanglement Negativity in Holographic Field Theories
• Holographic entanglement entropy and gravitational anomalies
• Conformal Blocks and Negativity at Large Central Charge
• Brown-Henneaux's Canonical Approach to Topologically Massive Gravity
• Holographic Quantum Entanglement Negativity
• Some Aspects of Entanglement Wedge Cross-Section
• Holographic entanglement negativity and replica symmetry breaking
• Entanglement negativity, Holography and Black holes
• Balanced Partial Entanglement and the Entanglement Wedge Cross Section
• Reflected Entropy and Entanglement Wedge Cross Section with the First Order Correction
• Entanglement negativity at large central charge
• Holographic entanglement negativity conjecture for adjacent intervals in $Ad{S}_3/CF{T}_2$
• Holographic Entanglement Negativity for Adjacent Subsystems in $\mathrm{Ad}{\mathrm{S}}_{\mathrm{d}+1}/CF{\mathrm{T}}_{\mathrm{d}}$
• Covariant holographic entanglement negativity
• Covariant Holographic Entanglement Negativity for Adjacent Subsystems in $\mathrm{Ad}{\mathrm{S}}_3/CF{\mathrm{T}}_2$
• Covariant holographic entanglement negativity for disjoint intervals in $Ad{S}_3/CF{T}_2$
• Page Curve for Entanglement Negativity through Geometric Evaporation
• Entanglement negativity in Galilean conformal field theories
• Holographic entanglement negativity for disjoint intervals in $Ad{S}_3/CF{T}_2$
• Evolution of Entanglement Wedge Cross Section Following a Global Quench
• Holographic Entanglement Negativity for Conformal Field Theories with a Conserved Charge
• Entanglement Wedge Cross Section in Holographic Excited States
• Time Evolution of Entanglement Negativity from Black Hole Interiors
• Holographic entanglement entropy in AdS${}_3$$/$WCFT
• Anomalous Gravitation and its Positivity from Entanglement
• The Markov gap for geometric reflected entropy

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• Holographic Study of Reflected Entropy in Anisotropic Theories
• Ownerless island and partial entanglement entropy in island phases
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• Reflected Entropy in AdS${}_3$/WCFT
• Entanglement negativity in $\text{T}\bar{\text{T}}$-deformed CFT${}_2$s
• Reflected Entropy and Entanglement Negativity for Holographic Moving Mirrors
• Entanglement Wedge Cross Section Growth During Thermalization
• Odd entanglement entropy in $\text{T}\bar{\text{T}}$ deformed CFT${}_2$s and holography
• Mixed state information theoretic measures in boosted black brane
• Mixed state entanglement in deformed field theory at finite temperature
• Covariant holographic reflected entropy in $Ad{S}_3/CF{T}_2$
• Revisit the entanglement entropy with gravitational anomaly
• Covariant odd entanglement entropy in AdS${}_3$/CFT${}_2$
• Coarse-Grained Fixed-Point Tensor Networks and Holographic Reflected Entropy in 3D Gravity