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Ownerless island and partial entanglement entropy in island phases
by Debarshi Basu, Jiong Lin, Yizhou Lu, Qiang Wen
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Submission summary
| Authors (as registered SciPost users): | Debarshi Basu · Qiang Wen |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202308_00014v2 (pdf) |
| Date accepted: | 2023-11-21 |
| Date submitted: | 2023-11-11 06:54 |
| Submitted by: | Wen, Qiang |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
In the context of partial entanglement entropy (PEE), we study the entanglement structure of the island phases realized in several 2-dimensional holographic set-ups. From a pure quantum information perspective, the entanglement islands emerge from the self-encoding property of the system, which gives us new insights on the construction of the PEE and the physical interpretation of two-point functions of twist operators in island phases. With the contributions from the entanglement islands properly taken into account, we give a generalized prescription to construct PEE and balanced partial entanglement entropy (BPE). Here the ownerless island region, which lies inside the island $\text{Is}(AB)$ of $A\cup B$ but outside $\text{Is}(A)\cup \text{Is}(B)$, plays a crucial role. Remarkably, we find that under different assignments for the ownerless island, we get different BPEs, which exactly correspond to different saddles of the entanglement wedge cross-section (EWCS) in the entanglement wedge of $A\cup B$. The assignments can be settled by choosing the one that minimizes the BPE. Furthermore, under this assignment we study the PEE and give a geometric picture for the PEE in holography, which is consistent with the geometric picture in the no-island phases.
List of changes
Dear Editor
According to the referee's reports, in this version we give more clarifications on the role played by the self-encoding property in this paper. Also we give more discussion on this property and give more future directions.
We re-wrote the first paragraph in page 4, section 7.2 and the second sentence in the abstract. These parts are marked blue.
Also a few references are added
The authors
Published as SciPost Phys. 15, 227 (2023)
Reports on this Submission
Report #1 by Anonymous (Referee 2) on 2023-11-13 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202308_00014v2, delivered 2023-11-13, doi: 10.21468/SciPost.Report.8101
Strengths
1- Clarified the rôle of the self-encoding property of the systems considered
Report
Dear Editor,
I thank the Authors for clarifying the rôle of the self-encoding property of the systems considered.
I now understand better their point of view, namely that, constraining the whole Hilbert space, it is possible to have non-gravitating (and truly non-holographic) systems for which an "Island Formula II" (as defined in the text) applies.
I now appreciate better that this point of view is quite original, and I agree with the Authors that it also suits laboratory implementations of systems following the "Island Formula II".
On the other hand, it is not clear whether the Hilbert space of gravitational systems is constrained in the same way as self-encoding systems. Consequently, the Authors have clarified the necessary assumptions needed for this to work, and identified future directions to resolve this issue.
Personally, I think one of the most interesting and pressing ones is (quoting the manuscript) "what are the constraints in gravitational systems that vastly reduce the Hilbert space, hence lead to the corresponding coding relation?"
Overall, I think that the manuscript has improved in clarity.