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.

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

References in corpus (13)

• Towards a derivation of holographic entanglement entropy
• Entanglement negativity in quantum field theory
• Deriving covariant holographic entanglement
• Entanglement entropy in Galilean conformal field theories and flat holography
• Finite temperature entanglement negativity in conformal field theory
• Semi-classical central charge in topologically massive gravity
• Black Hole Entropy in the presence of Chern-Simons Terms
• Comments on Entanglement Negativity in Holographic Field Theories
• Holographic entanglement entropy and gravitational anomalies
• Conformal Blocks and Negativity at Large Central Charge
• Some Aspects of Entanglement Wedge Cross-Section
• Evolution of Entanglement Wedge Cross Section Following a Global Quench
• The Markov gap for geometric reflected entropy

Cited by in corpus (16)

• Reflected entropy is not a correlation measure
• Covariant entanglement wedge cross-section, balanced partial entanglement and gravitational anomalies
• Holographic Study of Reflected Entropy in Anisotropic Theories
• Ownerless island and partial entanglement entropy in island phases
• Defect extremal surfaces for entanglement negativity
• 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