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 (22)

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Cited by in corpus (35)

• Islands for Reflected Entropy
• Entanglement Wedge Cross Sections Require Tripartite Entanglement
• Reflected Entropy for an Evaporating Black Hole
• Entanglement Wedge Cross Section from CFT: Dynamics of Local Operator Quench
• Defect Extremal Surface for Reflected Entropy
• Generalizations of Reflected Entropy and the Holographic Dual
• Reflected entropy, symmetries and free fermions
• Multipartite Purification, Multiboundary Wormholes and Islands in AdS${}_3$/CFT${}_2$
• Topological reflected entropy in Chern-Simons theories
• Islands for Entanglement Negativity
• Reflected entropy for free scalars
• Towards classification of holographic multi-partite entanglement measures
• Reflected entropy is not a correlation measure
• Entanglement Entropy after Double-Excitation as Interaction Measure
• Reflected Entropy in AdS${}_3$/WCFT
• CFT sewing as the dual of AdS cut-and-paste
• A Field Theory Study of Entanglement Wedge Cross Section: Odd Entropy
• Inequalities of Holographic Entanglement of Purification from Bit Threads
• Entanglement wedge cross-section in shock wave geometries
• Connections between reflected entropies and hyperbolic string vertices
• Bounding entanglement wedge cross sections
• Entanglement Wedge Cross Section Inequalities from Replicated Geometries
• On minimal entanglement wedge cross section for holographic entanglement negativity
• Multipartite entanglement and topology in holography
• Optimized Correlation Measures in Holography
• Reflected multi-entropy and its holographic dual
• A quantum information perspective on meson melting
• One-half reflected entropy is not a lower bound for entanglement of purification
• Warping Wormholes with Dust: a Metric Construction of the Python's Lunch
• The Markov gap for geometric reflected entropy
• Phase Transitions of Correlations in Black Hole Geometries
• Holographic multipartite entanglement structures in IR modified geometries
• Rényi Entanglement of Purification and Half Rényi Reflected Entropy in Free Scalar Theory
• Holographic Reflected Entropy: Islands and Defect Phases
• Coarse-Grained Fixed-Point Tensor Networks and Holographic Reflected Entropy in 3D Gravity