Towards classification of holographic multi-partite entanglement measures

Abstract

In this paper, we systematically study the measures of multi-partite entanglement with the aim of constructing those measures that can be computed in probe approximation in the holographic dual. We classify and count general measures as invariants of local unitary transformations. After formulating these measures in terms of permutation group elements, we derive conditions that a probe measure should satisfy and find a large class of solutions. These solutions are generalizations of the multi-entropy introduced in arXiv:2206.09723 . We derive their holographic dual with the assumption that the replica symmetry is unbroken in the bulk and check our prescription with explicit computations in $2d$ CFTs. Analogous to the multi-entropy, the holographic dual of these measures is given by the weighted area of the minimal brane-web but with branes having differing tensions. We discuss the replica symmetry assumption and also how the already known entanglement measures, such as entanglement negativity and reflected entropy fit in our framework.

arXiv comment55 pages, 24 figures ; modified the discussion in sections 1, 3, 4 and 7; added references and two figures

References in corpus (38)

• Quantum entanglement
• Gauge Theory Correlators from Non-Critical String Theory
• Holographic Derivation of Entanglement Entropy from AdS/CFT
• A Covariant Holographic Entanglement Entropy Proposal
• Generalized gravitational entropy
• Multi-party entanglement in graph states
• Quantum Extremal Surfaces: Holographic Entanglement Entropy beyond the Classical Regime
• Quantum corrections to holographic entanglement entropy
• Bulk Locality and Quantum Error Correction in AdS/CFT
• The Page curve of Hawking radiation from semiclassical geometry
• Holography from Conformal Field Theory
• Entanglement Renyi entropies in holographic theories
• Reconstruction of Bulk Operators within the Entanglement Wedge in Gauge-Gravity Duality
• Relative entropy equals bulk relative entropy
• The Ryu-Takayanagi Formula from Quantum Error Correction
• The Gravity Dual of Renyi Entropy
• Holographic Entanglement Entropy for General Higher Derivative Gravity
• Separable states are more disordered globally than locally
• Counting Gauge Invariants: the Plethystic Program
• Correlation functions for M^N/S_N orbifolds
• Holographic Calculations of Renyi Entropy
• On Holographic Entanglement Entropy and Higher Curvature Gravity
• Three-point functions for M^N/S^N orbifolds with N=4 supersymmetry
• Entropy, Extremality, Euclidean Variations, and the Equations of Motion
• Decoding the Apparent Horizon: A Coarse-Grained Holographic Entropy
• A new handle on three-point coefficients: OPE asymptotics from genus two modular invariance
• Entanglement of Purification for Multipartite States and its Holographic Dual
• Coarse Graining Holographic Black Holes
• A modular toolkit for bulk reconstruction
• Conditional and Multipartite Entanglements of Purification and Holography
• Generalizations of Reflected Entropy and the Holographic Dual
• Multipartite Reflected Entropy
• A new multi-partite entanglement measure and its holographic dual
• Multipartite Purification, Multiboundary Wormholes and Islands in AdS${}_3$/CFT${}_2$
• Fun with replicas: tripartitions in tensor networks and gravity
• Perturbative classical conformal blocks as Steiner trees on the hyperbolic disk
• Dynamics of a self-gravitating thin cosmic string
• Multipartite entanglement and topology in holography

Cited by in corpus (12)

• Symmetry-resolved Entanglement Entropy, Spectra & Boundary Conformal Field Theory
• Multi-entropy at low Renyi index in 2d CFTs
• Monotonicity conjecture for multi-party entanglement I
• Multi wavefunction overlap and multi entropy for topological ground states in (2+1) dimensions
• Towards a complete classification of holographic entropy inequalities
• Reflected multi-entropy and its holographic dual
• Entanglement Negativity and Replica Symmetry Breaking in General Holographic States
• Purely GHZ-like entanglement is forbidden in holography
• Holographic multipartite entanglement structures in IR modified geometries
• Black hole as a multipartite entangler: multi-entropy in AdS${}_3$/CFT${}_2$
• Upper bound of holographic entanglement entropy combinations
• Symmetry-resolved genuine multi-entropy: Haar random and graph states