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Two infinite families of facets of the holographic entropy cone
by Bartlomiej Czech, Yu Liu, Bo Yu
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Submission summary
| Authors (as registered SciPost users): | Bartek Czech |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2401.13029v4 (pdf) |
| Date accepted: | 2024-09-09 |
| Date submitted: | 2024-08-26 03:16 |
| Submitted by: | Czech, Bartek |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We verify that the recently proven infinite families of holographic entropy inequalities are maximally tight, i.e. they are facets of the holographic entropy cone. The proof is technical but it offers some heuristic insight. On star graphs, both families of inequalities quantify how concentrated / spread information is with respect to a dihedral symmetry acting on subsystems. In addition, toric inequalities viewed in the K-basis show an interesting interplay between four-party and six-party perfect tensors.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Author comments upon resubmission
We have implemented all changes suggested by the reviewers.
List of changes
Changes suggested by Referee 1 (report from 2024-5-6):
(1) A typo - We fixed it. Thank you for noticing it!
(2) We have significantly expanded the caption of Figure 5, including the explanation suggested by the Referee.
(3) Unusual phrasings - We changed four arguably extravagant phrasings, including the two listed by the Referee. They can be found in the source text marked with %###A3
Changes suggested by Referee 2 (report from 2024-the 8-11):
(1) We have completely rewritten the first 1.5 pages of the Introduction, following the route suggested by the Referee.
(a) We now introduce the holographic entropy cone before marginality, as suggested by the Referee.
(b) We now specify that marginality wrt one inequality requires consistency with all other inequalities, see the new equation (1.6). The referee further suggested writing "for a single i" instead of "for some i" in that equation. We retained "for some i" but added an explanatory sentence in the text leading up to (1.6). The new sentence reads: "Less generic ways to achieve marginality occur on intersections of facets, which form higher codimension loci in entropy space." We think this sentence should avert any confusion.
(c) We emphasize non-redundancy and discuss strong subadditivity as an example of a redundant inequality, exactly as suggested by the Referee.
(2) We now give a comprehensive account of which previously known facets are subsumed by our infinite families. We have also added a footnote, which explains why there is no overlap between the facets we verify (N odd) and those discovered in [14] (N=6; Ref. [12] in the previous version). A minor explanation: the mismatch between the assumed values of N is the reason why we previously had not listed Ref. [14] in this passage.
(3) We have added a footnote, which explains what was previously known about the facetness of the dihedral inequalities.
(4) Lemmas not in a mathematical form - We believe we fixed this. What was originally written as Lemma 1, 2, 3 had the least lemma-like appearance; we now cast the same assertions as Fact 1, 2, 3. In the new Lemma 2 (previously Lemma 5), we separated the definitions of "non-saturating AAAB-vectors" and "non-saturating ABBB-vectors" from the actual lemma. In multiple lemmas, we changed the writing so that a clear "Then..." statement announces the predicate.
(5) We removed all instances of "codimension-2 hyperplane"; they are now "codimension-2 subspaces".
(6) We added "in the span of K4-vectors" exactly as suggested.
(7) We removed the two appearances of $\mathbb{RP}^2$ and used "projective plane inequalities" instead.
Published as SciPost Phys. 17, 084 (2024)