Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2205.07905 · Physical review. D/Physical review. D.

Defect extremal surfaces for entanglement negativity

Debarshi Basu, Himanshu Parihar, Vinayak Raj, Gautam Sengupta

Published Nov 7, 2023• 14 citations
arXivHTMLPDF

Abstract

We propose a doubly holographic version of the semiclassical island formula for the entanglement negativity in the framework of the defect AdS/BCFT correspondence where the anti--de Sitter (AdS) bulk contains a defect conformal matter theory. In this context, we propose a defect extremal surface (DES) formula for computing the entanglement negativity modified by the contribution from the defect matter theory on the end-of-the-world brane. The equivalence of the DES proposal and the semiclassical island formula for the entanglement negativity is demonstrated in ${\mathrm{AdS}}_{3}/{\mathrm{BCFT}}_{2}$ framework. Furthermore, in the time-dependent ${\mathrm{AdS}}_{3}/{\mathrm{BCFT}}_{2}$ scenarios involving eternal black holes in the lower dimensional effective description, we investigate the time evolution of the entanglement negativity through the DES and the island formulas and obtain the analogs of the Page curves.

DOI
10.1103/physrevd.108.106005

Related papers

Entanglement negativity and defect extremal surface

Yilu Shao, Ma-Ke Yuan, Yang Zhou

We study entanglement negativity for evaporating black hole based on the holographic model with defect brane. We introduce a defect extremal surface formula for entanglement negativity. Based on partial reduction, we show the equivalence between defect extremal surface formula and island formula for entanglement negativity in AdS _3 3 /BCFT _2 2 . Extending the study to the model of eternal black hole plus CFT bath, we find that black hole-black hole negativity decreases until vanishing, left black hole-left radiation negativity is always a constant, radiation-radiation negativity increases and then saturates at a time later than Page time. In all the time dependent cases, defect extremal surface formula agrees with island formula.

arXiv:2206.05951•SciPost Physics Core•May 8, 2024•5 citations

Defect extremal surface for reflected entropy

Tianyi Li, Ma-Ke Yuan, Yang Zhou

A bstract Defect extremal surface is defined by extremizing the Ryu-Takayanagi formula corrected by the quantum defect theory. This is interesting when the AdS bulk contains a defect brane (or string). We introduce a defect extremal surface formula for reflected entropy, which is a mixed state generalization of entanglement entropy measure. Based on a decomposition procedure of an AdS bulk with a brane, we demonstrate the equivalence between defect extremal surface formula and island formula for reflected entropy in AdS 3 /BCFT 2 . We also compute the evolution of reflected entropy in evaporating black hole model and find that defect extremal surface formula agrees with island formula.

arXiv:2108.08544•Journal of High Energy Physics•Jan 1, 2022•47 citations

Holographic reflected entropy: islands and defect phases

Ankur Dey, Gautam Sengupta

A bstract We investigate the mixed state entanglement structure through the reflected entropy for disjoint radiation subsystems coupled to a 2d eternal brane world black hole in a time dependent defect AdS 3 /BCFT 2 scenario. Utilizing the island prescription and the defect extremal surface (DES) formula, we demonstrate a complex mixed state entanglement structure through the reflected entropy corresponding to distinct entanglement entropy phases. In each case we verify the holographic duality of the reflected entropy with the bulk entanglement wedge cross section (EWCS) and also obtain the Page curves for both the entanglement entropy and the associated reflected entropy phases. Furthermore, we extend our analysis to adjacent radiation subsystems and obtain consistent results using both the island and the DES prescription.

arXiv:2509.06551•Journal of High Energy Physics•Dec 11, 2025•0 citations

Page curve from defect extremal surface and island in higher dimensions

Jinwei Chu, Feiyu Deng, Yang Zhou

Abstract Defect extremal surface (DES) is defined by minimizing the Ryu-Takayanagi surface corrected by the quantum theory localized on the defect, which is useful when the RT surface crosses or terminates on the defect. Based on the decomposition procedure of an AdS bulk with a defect brane, proposed in [69], we derive Page curve in a time dependent set up of AdS3/BCFT2, and find that the result from island formula agrees with defect extremal surface formula precisely. We then extend the study to higher dimensions and find that the entropy computed from bulk defect extremal surface is generally less than that from island formula in boundary low energy effective theory, which implies that the UV completion of island formula gives a smaller entropy.

arXiv:2105.09106•Journal of High Energy Physics•Oct 18, 2021•65 citations

Islands for entanglement negativity

Jaydeep Kumar Basak, Debarshi Basu, Vinay Malvimat +2 more

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.

arXiv:2012.03983•SciPost Physics•Jan 5, 2022•77 citations

Time evolution of entanglement negativity from black hole interiors

Vinay Malvimat, Sayid Mondal, Gautam Sengupta

Abstract We investigate the time evolution of entanglement negativity following a global quench for mixed state configurations of two disjoint and adjacent intervals in a (1 + 1)-dimensional conformal field theory (CFT 1+1) dual to the eternal black hole sliced in half by an end of the world brane, through the AdS 3 /CFT 2 correspondence. To this end we obtain the time evolution of the holographic entanglement negativity for such mixed states from a dual bulk eternal black hole geometry and elucidate the relevant geodesic structures. The holographic entanglement negativity for such mixed states, following a global quench is described by half of the results for the eternal black hole. Significantly our results exactly match with the corresponding CFT 1+1 computations.

arXiv:1812.04424•Journal of High Energy Physics•May 1, 2019•23 citations
We propose a doubly holographic version of the semiclassical island formula for the entanglement negativity in the framework of the defect AdS/BCFT correspondence where the anti--de Sitter (AdS) bulk contains a defect conformal matter theory. In this context, we propose a defect extremal surface (DES) formula for computing the entanglement negativity modified by the contribution from the defect matter theory on the end-of-the-world brane. The equivalence of the DES proposal and the semiclassical island formula for the entanglement negativity is demonstrated in AdS3/BCFT2{\mathrm{AdS}}_{3}/{\mathrm{BCFT}}_{2}AdS3​/BCFT2​ framework. Furthermore, in the time-dependent AdS3/BCFT2{\mathrm{AdS}}_{3}/{\mathrm{BCFT}}_{2}AdS3​/BCFT2​ scenarios involving eternal black holes in the lower dimensional effective description, we investigate the time evolution of the entanglement negativity through the DES and the island formulas and obtain the analogs of the Page curves.
We study entanglement negativity for evaporating black hole based on the holographic model with defect brane. We introduce a defect extremal surface formula for entanglement negativity. Based on partial reduction, we show the equivalence between defect extremal surface formula and island formula for entanglement negativity in AdS _3 3 /BCFT _2 2 . Extending the study to the model of eternal black hole plus CFT bath, we find that black hole-black hole negativity decreases until vanishing, left black hole-left radiation negativity is always a constant, radiation-radiation negativity increases and then saturates at a time later than Page time. In all the time dependent cases, defect extremal surface formula agrees with island formula.
A bstract Defect extremal surface is defined by extremizing the Ryu-Takayanagi formula corrected by the quantum defect theory. This is interesting when the AdS bulk contains a defect brane (or string). We introduce a defect extremal surface formula for reflected entropy, which is a mixed state generalization of entanglement entropy measure. Based on a decomposition procedure of an AdS bulk with a brane, we demonstrate the equivalence between defect extremal surface formula and island formula for reflected entropy in AdS 3 /BCFT 2 . We also compute the evolution of reflected entropy in evaporating black hole model and find that defect extremal surface formula agrees with island formula.
A bstract We investigate the mixed state entanglement structure through the reflected entropy for disjoint radiation subsystems coupled to a 2d eternal brane world black hole in a time dependent defect AdS 3 /BCFT 2 scenario. Utilizing the island prescription and the defect extremal surface (DES) formula, we demonstrate a complex mixed state entanglement structure through the reflected entropy corresponding to distinct entanglement entropy phases. In each case we verify the holographic duality of the reflected entropy with the bulk entanglement wedge cross section (EWCS) and also obtain the Page curves for both the entanglement entropy and the associated reflected entropy phases. Furthermore, we extend our analysis to adjacent radiation subsystems and obtain consistent results using both the island and the DES prescription.
Abstract Defect extremal surface (DES) is defined by minimizing the Ryu-Takayanagi surface corrected by the quantum theory localized on the defect, which is useful when the RT surface crosses or terminates on the defect. Based on the decomposition procedure of an AdS bulk with a defect brane, proposed in [69], we derive Page curve in a time dependent set up of AdS3/BCFT2, and find that the result from island formula agrees with defect extremal surface formula precisely. We then extend the study to higher dimensions and find that the entropy computed from bulk defect extremal surface is generally less than that from island formula in boundary low energy effective theory, which implies that the UV completion of island formula gives a smaller entropy.
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.
Abstract We investigate the time evolution of entanglement negativity following a global quench for mixed state configurations of two disjoint and adjacent intervals in a (1 + 1)-dimensional conformal field theory (CFT 1+1) dual to the eternal black hole sliced in half by an end of the world brane, through the AdS 3 /CFT 2 correspondence. To this end we obtain the time evolution of the holographic entanglement negativity for such mixed states from a dual bulk eternal black hole geometry and elucidate the relevant geodesic structures. The holographic entanglement negativity for such mixed states, following a global quench is described by half of the results for the eternal black hole. Significantly our results exactly match with the corresponding CFT 1+1 computations.