Bounding entanglement wedge cross sections

Abstract

The entanglement wedge cross sections (EWCSs) are postulated as dual gravity probes to certain measures for the entanglement of multiparty systems. We test various proposed inequalities for EWCSs. As it turns out, contrary to expectations, the EWCS is not clearly monogamous nor polygamous for tripartite systems but the results depend on the details and dimensionality of the geometry of the gravity solutions. We propose weaker monogamy relations for dual entanglement measures, which lead to a new lower bound on EWCS. Our work is based on a plethora of gravity backgrounds: pure anti de Sitter spaces, anti de Sitter black branes, those induced by a stack of Dp-branes, and cigar geometries in generic dimension.

35 pages, 19 figures, matches published version, references and discussion added

References in corpus (20)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Causality & holographic entanglement entropy
• A holographic proof of the strong subadditivity of entanglement entropy
• Monogamy Inequality in terms of Negativity for Three-Qubit States
• Holographic Entanglement of Purification from Conformal Field Theories
• Some Aspects of Entanglement Wedge Cross-Section
• Confinement, Phase Transitions and non-Locality in the Entanglement Entropy
• Holographic Entanglement Entropy of Multiple Strips
• Entanglement of Purification in Many Body Systems and Symmetry Breaking
• Multipartite Reflected Entropy
• Is entanglement a probe of confinement?
• On the interplay between magnetic field and anisotropy in holographic QCD
• Holographic Entanglement Entropy at Finite Temperature
• Balanced Partial Entanglement and Mixed State Correlations
• Holographic entanglement density for spontaneous symmetry breaking
• Holographic Study of Reflected Entropy in Anisotropic Theories
• Anisotropic Flows into Black Holes
• Entanglement Wedge Cross Section Inequalities from Replicated Geometries
• The Markov gap for geometric reflected entropy
• Entanglement wedge cross section inequalities in AdS/BCFT

Cited by in corpus (4)

• Ownerless island and partial entanglement entropy in island phases
• More on the upper bound of holographic n-partite information
• Mixed state entanglement in deformed field theory at finite temperature
• An analytic approach for holographic entanglement entropy at (quantum) criticality