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Quantum Extremal Surfaces and the Holographic Entropy Cone

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arxiv 2108.07280 v2 pith:HL2A7CW4 submitted 2021-08-16 hep-th gr-qcquant-ph

Chris Akers , Sergio Hernández-Cuenca , Pratik Rath This is my paper · ORCID
classification hep-thgr-qcquant-ph
keywords entropiesquantumentropybulkinequalitiesboundarysatisfycone
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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.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Hollow-grams: Generalized Entanglement Wedges from the Gravitational Path Integral

    hep-th 2025-06 conditional novelty 7.0 of 10

    The entropy of a bulk region in holographic states equals the generalized entropy of the smallest wedge containing it, derived from a replica path integral via a hollow-graphic construction.

  2. Minimax surfaces and the holographic entropy cone

    hep-th 2025-02 conditional novelty 7.0 of 10

    Stable minimax surfaces are shown to be HRT surfaces, the entanglement wedge is the smallest minimax homology region, and a cooperating time-sheet configuration would prove the equality of RT and HRT entropy cones.

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