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Islands for Entanglement Negativity

by Jaydeep Kumar Basak, Debarshi Basu, Vinay Malvimat, Himanshu Parihar and Gautam Sengupta

Submission summary

As Contributors: Jaydeep Kumar Basak · Debarshi Basu · Vinay Malvimat · Himanshu Parihar
Preprint link: scipost_202107_00024v1
Date submitted: 2021-07-14 10:30
Submitted by: Malvimat, Vinay
Submitted to: SciPost Physics
Academic field: Physics
  • High-Energy Physics - Theory
Approach: Theoretical


We advance two alternative proposals for the island contributions to the entanglement negativity of various pure and mixed state configurations in quantum field theories coupled to semiclassical gravity. The first construction involves the extremization of an algebraic sum of the generalized Renyi entropies of order half. The second proposal involves the extremization of the sum of the effective entanglement negativity of quantum matter fields and the backreacted area of a cosmic brane spanning the entanglement wedge cross section which also extremizes the generalized Renyi reflected entropy of order half. These proposals are utilized to obtain the island contributions to the entanglement negativity of various pure and mixed state configurations involving the bath systems coupled to extremal and non-extremal black holes in JT gravity demonstrating an exact match with each other. Furthermore, the results from both the proposals match precisely with the island contribution to half the Renyi reflected entropy of order half providing a strong consistency check. We then allude to a possible doubly holographic picture of our island proposals and provide a derivation of the first proposal by determining the corresponding replica wormhole contributions.

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Editor-in-charge assigned

Submission & Refereeing History

Reports on this Submission

Anonymous Report 2 on 2021-9-21 (Invited Report)


1 - Detailed, with lots of cases studied
2 - Pedagogical


1 - No insight has been provided for why the two different proposals are giving the same answer. If this insight is in one of the older papers, it still deserved to be written out.


The authors have presented two seemingly different proposals for computing the so-called entanglement negativity, a quantity that is a measure of quantum entanglement in mixed states. The authors have explained a lot of previous results, and have included a lot of details in many cases for which they computed the entanglement negativity using both their proposals.

Since the presence of entanglement islands for vN entropy is an exciting recent development, it makes sense to study island contributions to other entanglement measures. This paper is doing so.

I recommend publication after the minor changes below.

Requested changes

1 - Provide some plausible mechanism, perhaps to be proved in future, for why the two different proposals are giving the same answer.

2- In many places the italicization of multi-letter subscripts or superscripts is not consistent. The abbreviations gen, eff, or Is appear both in straight face and in italics. It would be better to adopt one consistent notation.

  • validity: top
  • significance: good
  • originality: good
  • clarity: top
  • formatting: excellent
  • grammar: perfect

Anonymous Report 1 on 2021-7-28 (Invited Report)


The authors of "Islands for Entanglement Negativity" employ two complementary proposals for studying contributions to entanglement negativity as a result from the island prescription. They perform this for pure and mixed state configurations of a large c CFT coupled to a semi-classical eternal AdS_{2} black hole, described using semi-classical JT gravity. Proposal-I is constructed from a combination of generalized Renyi entropies. Proposal-II is constructed using the entanglement wedge cross section. They find the proposals agree and provide a clear brane world picture of the on/off-set of the quantum extremal surface and its contribution to the entanglement. This work provides good opportunities for new research.

Furthermore, sufficient details are provided, also reference wise, and both abstract and introduction reflect the content of the paper.

I have few remarks:

- In the conclusion you refer to studying evaporating black holes. In terms of the setup you sketch in, e.g. the Penrose diagram in Figure 22, one will obtain a one sided black hole diagram with a black hole with finite lifetime. The time dependence will enter explicitly in the dilaton as well now as you're in the Unruh state. Where do you expect this will become difficult for you? In other words: what (if anything) is stopping you from doing this now?

- I'd like to point out where using a brane world perspective semi-classical corrections to the eternal BTZ black hole are computed. This would provide a nice context to test proposal I and II against each other.

- As you are looking at pure and mixed states I am wondering what you expect as an outcome for your proposals when applied to semi-classical two-dimensional de Sitter in the Bunch-Davies vacuum and different sides of cosmological horizon. Could you comment on that?

  • validity: -
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