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.

21 pages, 4 figures, 1 appendix, citations added in v2

References in corpus (8)

• Holography from Conformal Field Theory
• A holographic proof of the strong subadditivity of entanglement entropy
• Black hole entropy as entanglement entropy: a holographic derivation
• Gravity/Ensemble Duality
• Quantum Extremal Islands Made Easy, PartIII: Complexity on the Brane
• The holographic entropy arrangement
• On the foundations and extremal structure of the holographic entropy cone
• Quantum bit threads and holographic entanglement

Cited by in corpus (11)

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• Holographic spacetime, black holes and quantum error correcting codes: A review
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• 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