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Quantum Maximin Surfaces

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arxiv 1912.02799 v3 pith:7VIXUUNC submitted 2019-12-05 hep-th gr-qc

Chris Akers , Netta Engelhardt , Geoff Penington , Mykhaylo Usatyuk This is my paper · ORCID
classification hep-thgr-qc
keywords quantummaximinbulkentropyprescriptionentanglementextremalmaximinimization
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abstract

We formulate a quantum generalization of maximin surfaces and show that a quantum maximin surface is identical to the minimal quantum extremal surface, introduced in the EW prescription. We discuss various subtleties and complications associated to a maximinimization of the bulk von Neumann entropy due to corners and unboundedness and present arguments that nonetheless a maximinimization of the UV-finite generalized entropy should be well-defined. We give the first general proof that the EW prescription satisfies entanglement wedge nesting and the strong subadditivity inequality. In addition, we apply the quantum maximin technology to prove that recently proposed generalizations of the EW prescription to nonholographic subsystems (including the so-called "quantum extremal islands") also satisfy entanglement wedge nesting and strong subadditivity. Our results hold in the regime where backreaction of bulk quantum fields can be treated perturbatively in $G_{N}\hbar$, but we emphasize that they are valid even when gradients of the bulk entropy are of the same order as variations in the area, a regime recently investigated in new models of black hole evaporation in AdS/CFT.

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Cited by 4 Pith papers

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

  1. 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.

  2. Tests of restricted Quantum Focusing and a new CFT bound

    hep-th 2025-10 conditional novelty 6.0 of 10

    From rQFC, a new CFT bound follows that forbids the QNEC from saturating faster than O(Σ^{d−2}) in near-vacuum states, while rQFC is proven in JT gravity and explicit QFC counterexamples are constructed.

  3. An apologia for islands

    hep-th 2025-06 conditional novelty 6.0 of 10

    Entanglement islands and Page curves can arise in massless gravity without an external bath, and compactly supported gauge-invariant operators exist in islands around generic symmetry-breaking black hole backgrounds.

  4. Page Curve for an Evaporating Schwarzschild Black Hole in Dimensionally-Reduced Model of Dilaton Gravity

    hep-th 2025-07 conditional novelty 5.0 of 10

    In a dimensionally-reduced dilaton-gravity model, the island formula produces a Page curve for an evaporating Schwarzschild black hole, with the entropy vanishing at the endpoint.

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