Quantum Extremal Surfaces and the Holographic Entropy Cone

Abstract

Quantum states with geometric duals are known to satisfy a stricter set of entropy inequalities than those obeyed by general quantum systems. The set of allowed entropies derived using the Ryu-Takayanagi (RT) formula defines the Holographic Entropy Cone (HEC). These inequalities are no longer satisfied once general quantum corrections are included by employing the Quantum Extremal Surface (QES) prescription. Nevertheless, the structure of the QES formula allows for a controlled study of how quantum contributions from bulk entropies interplay with HEC inequalities. In this paper, we initiate an exploration of this problem by relating bulk entropy constraints to boundary entropy inequalities. In particular, we show that requiring the bulk entropies to satisfy the HEC implies that the boundary entropies also satisfy the HEC. Further, we also show that requiring the bulk entropies to obey monogamy of mutual information (MMI) implies the boundary entropies also obey MMI.

arXiv comment21 pages, 4 figures, 1 appendix, citations added in v2

References in corpus (54)

• Holographic Derivation of Entanglement Entropy from AdS/CFT
• The World as a Hologram
• A Covariant Holographic Entanglement Entropy Proposal
• Building up spacetime with quantum entanglement
• Replica Wormholes and the Entropy of Hawking Radiation
• Quantum Extremal Surfaces: Holographic Entanglement Entropy beyond the Classical Regime
• Quantum corrections to holographic entanglement entropy
• The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole
• The Page curve of Hawking radiation from semiclassical geometry
• The entropy of Hawking radiation
• Holography from Conformal Field Theory
• Holographic Dual of BCFT
• Reconstruction of Bulk Operators within the Entanglement Wedge in Gauge-Gravity Duality
• Holographic duality from random tensor networks
• Maximin Surfaces, and the Strong Subadditivity of the Covariant Holographic Entanglement Entropy
• Aspects of AdS/BCFT
• The Ryu-Takayanagi Formula from Quantum Error Correction
• Holographic Mutual Information is Monogamous
• A holographic proof of the strong subadditivity of entanglement entropy
• Massive Islands
• Entanglement islands in higher dimensions
• Bulk locality from modular flow
• Information radiation in BCFT models of black holes
• A Stereoscopic Look into the Bulk
• The Holographic Entropy Cone
• Bit threads and holographic entanglement
• Black hole entropy as entanglement entropy: a holographic derivation
• Gravity/Ensemble Duality
• Representation of matroids
• Entanglement Wedge Reconstruction via Universal Recovery Channels
• Quantum Extremal Islands Made Easy, PartIII: Complexity on the Brane
• Islands for Reflected Entropy
• Entanglement Wedge Cross Sections Require Tripartite Entanglement
• Learning the Alpha-bits of Black Holes
• Leading order corrections to the quantum extremal surface prescription
• The Holographic Entropy Cone for Five Regions
• Multipartite Entanglement in Stabilizer Tensor Networks
• On Spacetime Entanglement
• Holographic entropy relations
• Bit Threads and Holographic Monogamy
• Towards Bulk Metric Reconstruction from Extremal Area Variations
• A Holographic Entanglement Entropy Conjecture for General Spacetimes
• The holographic entropy arrangement
• Pulling the Boundary into the Bulk
• Holographic Entropy Relations Repackaged
• Holographic Entropy Cone with Time Dependence in Two Dimensions
• Superbalance of Holographic Entropy Inequalities
• On the foundations and extremal structure of the holographic entropy cone
• The Quantum Entropy Cone of Hypergraphs
• Maximin is Not Enough
• Hypergraph min-cuts from quantum entropies
• More of the Bulk from Extremal Area Variations
• A Gap Between the Hypergraph and Stabilizer Entropy Cones
• Quantum bit threads and holographic entanglement

Cited by in corpus (11)

• Quantum Information in Holographic Duality
• Holographic spacetime, black holes and quantum error correcting codes: A review
• A holographic inequality for $N=7$ regions
• The Symmetrized Holographic Entropy Cone
• The holographic entropy cone from marginal independence
• Tripartite information at long distances
• Topological Link Models of Multipartite Entanglement
• Quantum bit threads and holographic entanglement
• Entanglement entropy and vacuum states in Schwarzschild geometry
• Improved proof-by-contraction method and relative homologous entropy inequalities
• Entanglement wedge cross section inequalities in AdS/BCFT