A new multi-partite entanglement measure and its holographic dual

Abstract

In this letter we define a natural generalization of the von Neumann entropy to multiple parties that is symmetric with respect to all the parties. We call this measure multi-entropy. We show that for conformal field theories with holographic duals, the multi-entropy is computed by the area of an appropriate "soap-film" anchored on the boundary. We conjecture the quantum version of this prescription that takes into account the sub-leading corrections in G_N.

arXiv comment7 pages, 3 figures, added comments about the junction contributions and covariant generalization, added a discussion on analytic continuation

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• Monotonicity conjecture for multi-party entanglement I
• Multipartite edge modes and tensor networks
• Multi wavefunction overlap and multi entropy for topological ground states in (2+1) dimensions
• Aspects of N-partite information in conformal field theories
• More on the upper bound of holographic n-partite information
• Towards a complete classification of holographic entropy inequalities
• Entanglement Negativity and Replica Symmetry Breaking in General Holographic States
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• Black hole as a multipartite entangler: multi-entropy in AdS${}_3$/CFT${}_2$
• Entanglement Spectrum Resolved by Loop Symmetries