Multipartite Reflected Entropy

Abstract

We discuss two methods that, through a combination of cyclically gluing copies of a given $n$-party boundary state in AdS/CFT and a canonical purification, creates a bulk geometry that contains a boundary homologous minimal surface with area equal to 2 or 4 times the $n$-party entanglement wedge cross-section, depending on the parity of the party number and choice of method. The areas of the minimal surfaces are each dual to entanglement entropies that we define to be candidates for the $n$-party reflected entropy. In the context of AdS${}_3$/CFT${}_2$, we provide a boundary interpretation of our construction as a multiboundary wormhole, and conjecture that this interpretation generalizes to higher dimensions.

20 pages, 7 figures; added references, one figure, and expanded discussion on black holes and the boundary state

References in corpus (1)

• Holographic Entanglement of Purification from Conformal Field Theories

Cited by in corpus (7)

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• Entanglement wedge cross-section in shock wave geometries
• Connections between reflected entropies and hyperbolic string vertices
• Entanglement Wedge Cross Section Inequalities from Replicated Geometries
• The Markov gap for geometric reflected entropy
• Warping Wormholes with Dust: a Metric Construction of the Python's Lunch
• Phase Transitions of Correlations in Black Hole Geometries