SciPost Submission Page
One-shot holography
by Chris Akers, Adam Levine, Geoff Penington, Elizabeth Wildenhain
Submission summary
| Ontological classification |
| Academic field: |
Physics |
| Specialties: |
- High-Energy Physics - Theory
- Quantum Physics
|
| Approach: |
Theoretical |
Abstract
Following the work of [2008.03319], we define a generally covariant max-entanglement wedge of a boundary region $B$, which we conjecture to be the bulk region reconstructible from $B$. We similarly define a covariant min-entanglement wedge, which we conjecture to be the bulk region that can influence the state on $B$. We prove that the min- and max-entanglement 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 one-shot versions of the (restricted) quantum focusing conjecture (QFC) that we conjecture to hold. We argue that these QFCs imply a one-shot generalized second law (GSL) and quantum Bousso bound. Moreover, in a particular semiclassical limit we prove this one-shot GSL directly using algebraic techniques. Finally, in order to derive our results, we extend both the frameworks of one-shot quantum Shannon theory and state-specific reconstruction to finite-dimensional von Neumann algebras, allowing nontrivial centers.
Author comments upon resubmission
We thank the reviewers for their helpful comments and have implemented the suggested changes.
List of changes
1. We added a sentence explaining the meaning of q \le p above definition 2.14
2. Immediately prior to the definitions in section 3.1, we indicate a section of a reference that contains figures for each definition.
3. We included a footnote in the introduction stating an example of a state in semiclassical gravity where the min- and max-entanglement wedges are not identical and the entanglement wedge is not well-defined.
