Towards a Bit Threads Derivation of Holographic Entanglement of Purification

Abstract

We apply the bit thread formulation of holographic entanglement entropy to reduced states describing only the geometry contained within an entanglement wedge. We argue that a certain optimized bit thread configuration, which we construct, gives a purification of the reduced state to a full holographic state obeying a precise set of conditional mutual information relations. When this purification exists, we establish, under certain assumptions, the conjectured $E_P=E_W$ relation equating the entanglement of purification with the area of the minimal cross section partitioning the bulk entanglement wedge. Along the way, we comment on minimal purifications of holographic states, geometric purifications, and black hole geometries.

29 pages, 7 figures

References in corpus (6)

• Surface/State Correspondence as a Generalized Holography
• Geometric Aspects of Holographic Bit Threads
• Entanglement of Purification for Multipartite States and its Holographic Dual
• Coarse Graining Holographic Black Holes
• Holographic Inequalities and Entanglement of Purification
• Entanglement of Purification and Multiboundary Wormhole Geometries

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• Entanglement Wedge in Flat Holography and Entanglement Negativity
• Balanced Partial Entanglement and Mixed State Correlations
• Correlation measures and distillable entanglement in AdS/CFT
• The Quantum Entropy Cone of Hypergraphs
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• More of the Bulk from Extremal Area Variations
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• Multipartite Optimized Correlation Measures and Holography
• Optimized Correlation Measures in Holography
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