Entanglement of Purification in Holographic Systems

Abstract

The holographic entanglement of purification (EoP) in AdS${}_4$ and AdS-RN black hole backgrounds is studied. We develop an algorithm to compute the EoP for bipartite configuration with infinitely long strips. The temperature behavior of EoP is revealed for small, intermediate and large configurations: EoP monotonically increases with the temperature for small configurations; while for intermediate configurations, EoP is configuration-dependent; EoP vanishes for large configurations. Our numerical results verify some important inequalities of EoP, which we also prove geometrically in Poincaré coordinate.

27 pages, 14 figures; minor revision, ref added; major revision, the version appeared on JHEP

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• Reflected Entropy in Double Holography
• Aspects of Hyperscaling Violating Geometries at Finite Cutoff
• Mixed state entanglement measures as probe for confinement
• Islands for Entanglement Negativity
• Long-distance entanglement of purification and reflected entropy in conformal field theory
• Holographic Study of Reflected Entropy in Anisotropic Theories
• Evolutions of entanglement and complexity after a thermal quench in massive gravity theory
• Holographic subregion complexity under thermal quench in Einstein-Maxwell-Axions theory with momentum relaxation
• Mixed State Entanglement and Thermal Phase Transitions
• Informational properties for Einstein-Maxwell-Dilaton Gravity
• Informational properties of holographic Lifshitz field theory
• Inequalities of Holographic Entanglement of Purification from Bit Threads
• Entanglement wedge cross-section in shock wave geometries
• Entanglement Wedge Minimum Cross-Section for Holographic Aether Gravity
• Improved proof-by-contraction method and relative homologous entropy inequalities
• Non-Conformal Behavior of Holographic Entanglement Measures
• Entanglement wedge cross section inequalities in AdS/BCFT