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:2206.05951 · SciPost Physics Core

Entanglement negativity and defect extremal surface

Yilu Shao, Ma-Ke Yuan, Yang Zhou

Published May 8, 2024• 5 citations
arXivHTMLPDF

Abstract

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.

DOI
10.21468/scipostphyscore.7.2.027

Related papers

Defect extremal surfaces for entanglement negativity

Debarshi Basu, Himanshu Parihar, Vinayak Raj +1 more

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.

arXiv:2205.07905•Physical review. D/Physical review. D.•Nov 7, 2023•14 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

Islands for entanglement negativity in communicating black holes

Mir Afrasiar, Jaydeep Kumar Basak, Ashish Chandra +1 more

We obtain the holographic entanglement negativity for bipartite mixed states at a finite temperature in baths described by conformal field theories dual to configurations involving two communicating black holes in a braneworld geometry. In this context, we analyze the mixed state entanglement structure characterized by the information transfer between the black holes. The model corresponds to a configuration of two dimensional eternal Jackiw-Teitelboim (JT) black holes in a braneworld geometry involving two Planck branes coupled through shared bath systems described by ${\mathrm{CFT}}_{2}\mathrm{s}$. Our results reproduce analogue of the Page curves for the entanglement negativity obtained earlier in the context of random matrix theory and from geometric evaporation in JT black hole configurations.

arXiv:2205.07903•Physical review. D/Physical review. D.•Sep 20, 2023•18 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

Effective reflected entropy and entanglement negativity for general 2D eternal black holes

Jiong Lin, Yizhou Lu

Both reflected entropy and entanglement negativity provide valid measures of entanglement between subsystems of a mixed state. For general 2D eternal black holes coupled with CFT matters in large $c$ limit, we perform the replica-trick computation and find that both effective Renyi reflected entropy and effective entanglement negativity can be expressed in terms of the combination of modified backreacting cosmic branes in $\mathrm{AdS}_3$ bulk. We then develop a holographic scheme to calculate effective reflected entropy and entanglement negativity for general 2D eternal black holes coupled with CFT matters in large $c$ limit. Using the scheme, we check the consistency condition of the island formulae for entanglement negativity and reflected entropy. We find that the combinations of modified backreacting cosmic branes in $\mathrm{AdS}_3$ bulk from the two island proposals of entanglement negativity exactly match with each other. Finally, we study the saturation of the reflected entropy inequality.

arXiv:2204.08290•Apr 18, 2022•3 citations
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.
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.
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.
We obtain the holographic entanglement negativity for bipartite mixed states at a finite temperature in baths described by conformal field theories dual to configurations involving two communicating black holes in a braneworld geometry. In this context, we analyze the mixed state entanglement structure characterized by the information transfer between the black holes. The model corresponds to a configuration of two dimensional eternal Jackiw-Teitelboim (JT) black holes in a braneworld geometry involving two Planck branes coupled through shared bath systems described by CFT2s{\mathrm{CFT}}_{2}\mathrm{s}CFT2​s. Our results reproduce analogue of the Page curves for the entanglement negativity obtained earlier in the context of random matrix theory and from geometric evaporation in JT black hole configurations.
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.
Both reflected entropy and entanglement negativity provide valid measures of entanglement between subsystems of a mixed state. For general 2D eternal black holes coupled with CFT matters in large ccc limit, we perform the replica-trick computation and find that both effective Renyi reflected entropy and effective entanglement negativity can be expressed in terms of the combination of modified backreacting cosmic branes in AdS3\mathrm{AdS}_3AdS3​ bulk. We then develop a holographic scheme to calculate effective reflected entropy and entanglement negativity for general 2D eternal black holes coupled with CFT matters in large ccc limit. Using the scheme, we check the consistency condition of the island formulae for entanglement negativity and reflected entropy. We find that the combinations of modified backreacting cosmic branes in AdS3\mathrm{AdS}_3AdS3​ bulk from the two island proposals of entanglement negativity exactly match with each other. Finally, we study the saturation of the reflected entropy inequality.