Entanglement Wedge Cross Section from the Dual Density Matrix

2018/09/30 by Kotaro Tamaoka · 164 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Conformal field theory #Conformal map #Conjecture #Cosmology and Gravitation Theories #Entropy (arrow of time) #Geometry #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Optics #Physics #Pure mathematics #Quantum #Quantum entanglement #Quantum mechanics #Replica trick #Theoretical physics #Wedge (geometry) #cond-mat.str-el #hep-th #quant-ph

paper · pdf · doi:10.1103/physrevlett.122.141601

published in Physical Review Letters 122(14), 141601 (American Physical Society) · 6 pages, Revtex, 2 figures. v2: shorter version for Physical Review Letters

openalex publication_date 2019/04/09 · arxiv created 2019/04/11 · arxiv updated 2019/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We define a new information theoretic quantity called odd entanglement entropy (OEE) which enables us to compute the entanglement wedge cross section in holographic conformal field theories (CFTs). The entanglement wedge cross section has been introduced as a minimal cross section of the entanglement wedge, a natural generalization of the Ryu-Takayanagi surface. By using the replica trick, we explicitly compute the OEE for two-dimensional holographic CFT (three-dimensional anti-de Sitter space and planar Bañados-Teitelboim-Zanelli black hole) and see agreement with the entanglement wedge cross section. We conjecture this relation will hold in general dimensions.

Citations

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