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Oneshot holography
by Chris Akers, Adam Levine, Geoff Penington, Elizabeth Wildenhain
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Submission summary
Authors (as registered SciPost users):  Christopher Akers 
Submission information  

Preprint Link:  https://arxiv.org/abs/2307.13032v1 (pdf) 
Date submitted:  20231103 01:29 
Submitted by:  Akers, Christopher 
Submitted to:  SciPost Physics 
Ontological classification  

Academic field:  Physics 
Specialties: 

Approach:  Theoretical 
Abstract
Following the work of [2008.03319], we define a generally covariant maxentanglement wedge of a boundary region $B$, which we conjecture to be the bulk region reconstructible from $B$. We similarly define a covariant minentanglement wedge, which we conjecture to be the bulk region that can influence the boundary state on $B$. We prove that the min and maxentanglement wedges obey various properties necessary for this conjecture, such as nesting, inclusion of the causal wedge, and a reduction to the usual quantum extremal surface prescription in the appropriate special cases. These proofs rely on oneshot versions of the (restricted) quantum focusing conjecture (QFC) that we conjecture to hold. We argue that this QFC implies a oneshot generalized second law (GSL) and quantum Bousso bound. Moreover, in a particular semiclassical limit we prove this oneshot GSL directly using algebraic techniques. Finally, in order to derive our results, we extend both the frameworks of oneshot quantum Shannon theory and statespecific reconstruction to finitedimensional von Neumann algebras, allowing nontrivial centers.
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Reports on this Submission
Report #2 by Anonymous (Referee 2) on 2024322 (Contributed Report)
 Cite as: Anonymous, Report on arXiv:2307.13032v1, delivered 20240322, doi: 10.21468/SciPost.Report.8733
Report
This paper explores the reconstruction of bulk subregions from the boundary, in the context of AdS/CFT correspondence. The authors attempt to refine the entanglement wedge reconstruction by defining “minentanglement wedge” and “max entanglement wedge”. Given a boundary subregion B, the authors conjecture that maxEW(B) is the largest bulk region (b) such that all information within b can be reconstructed from the boundary region B. Whereas, the minEW(B) is the smallest bulk region (b) such that no information outside b can be reconstructed from the boundary region B. Usually, we expect these wedges to be identical. However, the authors point that there are states in semiclassical gravity where entanglement wedge doesn’t exists and in such situations, the min and max entanglement wedges do not overlap. It would be helpful if authors include some examples or details of semiclassical states where the entanglement wedge doesn't exist.
The covariant definition of min and max entanglement wedges provided by the authors are based on the oneshot min and max quantum entropies. The authors define the oneshot entropies and study their properties in details. They also extend some known results to finite dimensional vonNeumann algebras.
In order to support the conjectured interpretation of max and min EW, the authors prove various consistency conditions. They show that in the cases where min and max EW coincides, the two wedges equal the entanglement wedge. According to the conjecture, all information within maxEW can be reconstructed from the boundary subregion, whereas, no information outside minEW can be reconstructed. This is consistent, only if maxEW is contained inside minEW, a result that the authors prove. The authors also show that maxEW contains the causal wedge and that the maxentanglement wedges show a nested structure that is, if A is contained in B, then maxEW[A] is contained in maxEW[B]. The proofs of these properties required the authors to assume a version of quantum focusing conjecture, that they explain in the paper.
Overall, the main results of the paper are conjectural, but interesting.
Requested changes
1. Explain the notation q \le p for operators p and q in definition 2.14. How is the ordering defined?
2. Authors may consider including a diagram to illustrate the definitions of wedge, wedge union and edge of the wedge in section 3.1.
3. Though they have provided references, the authors may consider including some examples of states in semiclassical gravity where the min and max entanglement wedges are not identical and the entanglement wedge doesn't exist.
Report #1 by Anonymous (Referee 1) on 2024321 (Invited Report)
 Cite as: Anonymous, Report on arXiv:2307.13032v1, delivered 20240321, doi: 10.21468/SciPost.Report.8720
Report
Conditions like the generalized second law and the more recent (restricted) quantum focusing are believed to be fundamental consistency conditions in the semiclassical limit of quantum gravity. In AdS/CFT, these conditions imply that entanglement wedges of nested boundary CFT regions nest in the bulk, upholding CFT causality. In arXiv:2008.03319, subregion duality on timesymmetric bulk slices in AdS/CFT was refined: in general, the codimension2 boundary between parts of the bulk which are fully encoded in one boundary subsystem and parts which are not was argued to have a certain vanishing "oneshot quantum expansion". If this is correct, it is then very important to find general (beyond timesymmetric slices) definitions of these codimension2 boundaries. It would then be very plausible that conditions analogous to (restricted) quantum focusing exists to uphold the consistency of this more refined bulktoboundary dictionary.
This paper accomplishes the task of providing fully covariant definitions of these refined bulk subregions. And appropriately, conjectures conditions analogous to QFC which upholds various consistency conditions of the dictionary. The paper is wellorganized and very clear. I therefore recommend it for publication as is