Entanglement Wedge Cross Section from the Dual Density Matrix

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 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 (AdS${}_3$ and planar BTZ blackhole) and see agreement with the entanglement wedge cross section. We conjecture this relation will hold in general dimensions.

6 pages, Revtex, 2 figures. v2: shorter version for Physical Review Letters

References in corpus (9)

• Entanglement negativity in quantum field theory
• Causality & holographic entanglement entropy
• Entanglement Entropy at Large Central Charge
• Entanglement negativity and minimal entanglement wedge cross sections in holographic theories
• Finite temperature entanglement negativity in conformal field theory
• The Entanglement Renyi Entropies of Disjoint Intervals in AdS/CFT
• Holographic Holes in Higher Dimensions
• Holographic Holes and Differential Entropy
• Nuts and Bolts for Creating Space

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