Local measures of entanglement in black holes and CFTs

Abstract

We study the structure and dynamics of entanglement in CFTs and black holes. We use a local entanglement measure, the entanglement contour, which is a spatial density function for von Neumann entropy with some additional properties. The entanglement contour can be calculated in many 1+1d condensed matter systems and simple models of black hole evaporation. We calculate the entanglement contour of a state excited by a splitting quench, and find universal results for the entanglement contours of low energy non-equilibrium states in 2d CFTs. We also calculate the contour of a non-gravitational bath coupled to an extremal AdS${}_2$ black hole, and find that the contour only has finite support within the bath, due to an island phase transition. The particular entanglement contour proposal we use quantifies how well the bath's state can be reconstructed from its marginals, through its connection to conditional mutual information, and the vanishing contour is a reflection of the protection of bulk island regions against erasures of the boundary state.

35 pages, 8 figures. v2: minor corrections and clarifications

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Cited by in corpus (11)

• Balanced Partial Entanglement and Mixed State Correlations
• The PEE aspects of entanglement islands from bit threads
• Microcanonical Action and the Entropy of Hawking Radiation
• Covariant entanglement wedge cross-section, balanced partial entanglement and gravitational anomalies
• Ownerless island and partial entanglement entropy in island phases
• Quantum bit threads
• Geometrizing the Partial Entanglement Entropy: from PEE Threads to Bit Threads
• Ergotropy and entanglement in critical spin chains
• Weaving the (AdS) spaces with partial entanglement entropy threads
• Bulk reconstruction of AdS${}_{d+1}$ metrics and developing kinematic space
• Holographic Tensor Networks as Tessellations of Geometry