Quantum maximin surfaces
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13130_2020_Article_13671.pdf
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Author(s)
Akers, Chris
Engelhardt, Netta
Penington, Geoff
Usatyuk, Mykhaylo
Date Issued
August 27, 2020
Publisher
Springer Berlin Heidelberg
Citation
Journal of High Energy Physics. 2020 Aug 27;2020(8):140
Version
Final published version
Abstract
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 GNħ, 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.
MIT Department
Massachusetts Institute of Technology. Center for Theoretical Physics
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DOI of Published Version
https://doi.org/10.1007/JHEP08(2020)140
