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:2610.13900

Reflected entropy and islands in JT gravity from partial dimensional reduction

Debarshi Basu, Himanshu Chourasiya

Published Oct 9, 2026• 0 citations
arXivHTMLPDF

Abstract

We study how mixed-state correlations reorganize across island transitions in Jackiw-Teitelboim gravity coupled to a non-gravitating bath. Using the partial-dimensional-reduction realization of double holography, we compute reflected entropy for adjacent and disjoint radiation regions in the vacuum and in the thermofield-double state of an eternal black hole. Reflected entropy probes the internal partition of the entanglement wedge and therefore resolves structure that is invisible to the ordinary Page curve: its dominant saddle can change even when the entropy saddle of the union remains fixed, and it vanishes at leading order when the entanglement wedge disconnects. We show that the lower-dimensional reflected-island description agrees, to leading order in the dynamical brane fluctuation, with the higher-dimensional defect-extremal-surface picture. The finite-angle comparison further suggests a projection-covariant identification of island and brane endpoints at linear order. The resulting Page-like curves and Markov gaps provide a geometric probe of the reorganization of the purification and of non-Markovian, multipartite correlation structure during island transitions.

DOI
10.48550/arxiv.2610.13900

Related papers

Holographic reflected entropy and islands in interface CFTs

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

A bstract We investigate the reflected entropy for various mixed state configurations in the two dimensional holographic conformal field theories sharing a common interface (ICFTs). In the AdS 3 /ICFT 2 framework, we compute the holographic reflected entropy for the required configurations in the vacuum state of the ICFT 2 which is given by twice the entanglement wedge cross section (EWCS) in a spacetime involving two AdS 3 geometries glued along a thin interface brane. Subsequently, we evaluate the EWCS in the bulk geometry involving eternal BTZ black strings with an AdS 2 interface brane, which is dual to an ICFT 2 in the thermofield double (TFD) state. We explore the system from a doubly holographic perspective and determine the island contributions to the reflected entropy in the two dimensional semi-classical description involving two CFT 2 s coupled to an AdS 2 brane. We demonstrate that the results from the island formula match precisely with the bulk AdS 3 results in the large tension limit of the interface brane. We illustrate that the phase structure of the reflected entropy is quite rich involving many novel induced island phases and demonstrate that it obeys the expected Page curve for the reflected entropy in a radiation bath coupled to the AdS 2 black hole.

arXiv:2312.12512•Journal of High Energy Physics•May 13, 2024•8 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

Bridging boundaries: $$ T\overline{T} $$, double holography, and reflected entropy

Debarshi Basu, Himanshu Chourasiya, Ankur Dey +1 more

A bstract We investigate the reflected entropy for bipartite mixed state configurations in a $$ T\overline{T} $$ T T ¯ deformed boundary conformal field theory in 2 dimensions (BCFT 2 ). The bulk dual is described by asymptotically AdS 3 geometries with the cut off surface pushed deeper into the bulk and truncated by an end of the world brane. We obtain the reflected entropy up to a linear order in the radial cut-off for static and time dependent configurations involving an eternal black hole, from the island and defect extremal surface (DES) prescriptions in the context of the deformed AdS/BCFT. We observe agreement of the leading order correction for all cases between the two prescriptions. We also obtain the analogous of the Page curves for the reflected entropy and investigate the modification due to the $$ T\overline{T} $$ T T ¯ deformation.

arXiv:2411.12827•Journal of High Energy Physics•Jun 17, 2025•6 citations

Reflected entropy for an evaporating black hole

Tianyi Li, Jinwei Chu, Yang Zhou

Abstract We study reflected entropy as a mixed state correlation measure in black hole evaporation. As a measure for bipartite mixed states, reflected entropy can be computed between black hole and radiation, radiation and radiation, and even black hole and black hole. We compute reflected entropy curves in three different models: 3-side wormhole model, End-of-the-World (EOW) brane model in three dimensions and two-dimensional eternal black hole plus CFT model. For 3-side wormhole model, we find that reflected entropy is dual to island cross section. The reflected entropy between radiation and black hole increases at early time and then decreases to zero, similar to Page curve, but with a later transition time. The reflected entropy between radiation and radiation first increases and then saturates. For the EOW brane model, similar behaviors of reflected entropy are found. We propose a quantum extremal surface for reflected entropy, which we call quantum extremal cross section. In the eternal black hole plus CFT model, we find a generalized formula for reflected entropy with island cross section as its area term by considering the right half as the canonical purification of the left. Interestingly, the reflected entropy curve between the left black hole and the left radiation is nothing but the Page curve. We also find that reflected entropy between the left black hole and the right black hole decreases and goes to zero at late time. The reflected entropy between radiation and radiation increases at early time and saturates at late time.

arXiv:2006.10846•Journal of High Energy Physics•Nov 1, 2020•104 citations

Ephemeral islands, plunging quantum extremal surfaces and BCFT channels

Timothy J. Hollowood, S. Prem Kumar, Andrea Legramandi +1 more

A bstract We consider entanglement entropies of finite spatial intervals in Minkowski radiation baths coupled to the eternal black hole in JT gravity, and the related problem involving free fermion BCFT in the thermofield double state. We show that the non-monotonic entropy evolution in the black hole problem precisely matches that of the free fermion theory in a high temperature limit, and the results have the form expected for CFTs with quasiparticle description. Both exhibit rich behaviour that involves at intermediate times, an entropy saddle with an island in the former case, and in the latter a special class of disconnected OPE channels. The quantum extremal surfaces start inside the horizon, but can emerge from and plunge back inside as time evolves, accompanied by a characteristic dip in the entropy also seen in the free fermion BCFT. Finally an entropy equilibrium is reached with a no-island saddle.

arXiv:2109.01895•Journal of High Energy Physics•Jan 1, 2022•23 citations

Reflected entropy in a BCFT on a black hole background

Debarshi Basu, Himanshu Chourasiya, Vinayak Raj +1 more

A bstract We obtain the reflected entropy for bipartite mixed state configurations involving two disjoint and adjacent subsystems in a two dimensional boundary conformal field theory (BCFT 2 ) in a black hole background. The bulk dual is described by an AdS 3 black string geometry truncated by a Karch-Randall brane. The entanglement wedge cross section computed for this geometry matches with the reflected entropy obtained for the BCFT 2 verifying the holographic duality. In this context, we also obtain the analogues of the Page curves for the reflected entropy and investigate the behaviour of the Markov gap.

arXiv:2311.17023•Journal of High Energy Physics•May 6, 2024•14 citations
We study how mixed-state correlations reorganize across island transitions in Jackiw-Teitelboim gravity coupled to a non-gravitating bath. Using the partial-dimensional-reduction realization of double holography, we compute reflected entropy for adjacent and disjoint radiation regions in the vacuum and in the thermofield-double state of an eternal black hole. Reflected entropy probes the internal partition of the entanglement wedge and therefore resolves structure that is invisible to the ordinary Page curve: its dominant saddle can change even when the entropy saddle of the union remains fixed, and it vanishes at leading order when the entanglement wedge disconnects. We show that the lower-dimensional reflected-island description agrees, to leading order in the dynamical brane fluctuation, with the higher-dimensional defect-extremal-surface picture. The finite-angle comparison further suggests a projection-covariant identification of island and brane endpoints at linear order. The resulting Page-like curves and Markov gaps provide a geometric probe of the reorganization of the purification and of non-Markovian, multipartite correlation structure during island transitions.
A bstract We investigate the reflected entropy for various mixed state configurations in the two dimensional holographic conformal field theories sharing a common interface (ICFTs). In the AdS 3 /ICFT 2 framework, we compute the holographic reflected entropy for the required configurations in the vacuum state of the ICFT 2 which is given by twice the entanglement wedge cross section (EWCS) in a spacetime involving two AdS 3 geometries glued along a thin interface brane. Subsequently, we evaluate the EWCS in the bulk geometry involving eternal BTZ black strings with an AdS 2 interface brane, which is dual to an ICFT 2 in the thermofield double (TFD) state. We explore the system from a doubly holographic perspective and determine the island contributions to the reflected entropy in the two dimensional semi-classical description involving two CFT 2 s coupled to an AdS 2 brane. We demonstrate that the results from the island formula match precisely with the bulk AdS 3 results in the large tension limit of the interface brane. We illustrate that the phase structure of the reflected entropy is quite rich involving many novel induced island phases and demonstrate that it obeys the expected Page curve for the reflected entropy in a radiation bath coupled to the AdS 2 black hole.
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.
Bridging boundaries: TT‾ T\overline{T} TT, double holography, and reflected entropy
A bstract We investigate the reflected entropy for bipartite mixed state configurations in a TT‾ T\overline{T} TT T T ¯ deformed boundary conformal field theory in 2 dimensions (BCFT 2 ). The bulk dual is described by asymptotically AdS 3 geometries with the cut off surface pushed deeper into the bulk and truncated by an end of the world brane. We obtain the reflected entropy up to a linear order in the radial cut-off for static and time dependent configurations involving an eternal black hole, from the island and defect extremal surface (DES) prescriptions in the context of the deformed AdS/BCFT. We observe agreement of the leading order correction for all cases between the two prescriptions. We also obtain the analogous of the Page curves for the reflected entropy and investigate the modification due to the TT‾ T\overline{T} TT T T ¯ deformation.
Abstract We study reflected entropy as a mixed state correlation measure in black hole evaporation. As a measure for bipartite mixed states, reflected entropy can be computed between black hole and radiation, radiation and radiation, and even black hole and black hole. We compute reflected entropy curves in three different models: 3-side wormhole model, End-of-the-World (EOW) brane model in three dimensions and two-dimensional eternal black hole plus CFT model. For 3-side wormhole model, we find that reflected entropy is dual to island cross section. The reflected entropy between radiation and black hole increases at early time and then decreases to zero, similar to Page curve, but with a later transition time. The reflected entropy between radiation and radiation first increases and then saturates. For the EOW brane model, similar behaviors of reflected entropy are found. We propose a quantum extremal surface for reflected entropy, which we call quantum extremal cross section. In the eternal black hole plus CFT model, we find a generalized formula for reflected entropy with island cross section as its area term by considering the right half as the canonical purification of the left. Interestingly, the reflected entropy curve between the left black hole and the left radiation is nothing but the Page curve. We also find that reflected entropy between the left black hole and the right black hole decreases and goes to zero at late time. The reflected entropy between radiation and radiation increases at early time and saturates at late time.
A bstract We consider entanglement entropies of finite spatial intervals in Minkowski radiation baths coupled to the eternal black hole in JT gravity, and the related problem involving free fermion BCFT in the thermofield double state. We show that the non-monotonic entropy evolution in the black hole problem precisely matches that of the free fermion theory in a high temperature limit, and the results have the form expected for CFTs with quasiparticle description. Both exhibit rich behaviour that involves at intermediate times, an entropy saddle with an island in the former case, and in the latter a special class of disconnected OPE channels. The quantum extremal surfaces start inside the horizon, but can emerge from and plunge back inside as time evolves, accompanied by a characteristic dip in the entropy also seen in the free fermion BCFT. Finally an entropy equilibrium is reached with a no-island saddle.
A bstract We obtain the reflected entropy for bipartite mixed state configurations involving two disjoint and adjacent subsystems in a two dimensional boundary conformal field theory (BCFT 2 ) in a black hole background. The bulk dual is described by an AdS 3 black string geometry truncated by a Karch-Randall brane. The entanglement wedge cross section computed for this geometry matches with the reflected entropy obtained for the BCFT 2 verifying the holographic duality. In this context, we also obtain the analogues of the Page curves for the reflected entropy and investigate the behaviour of the Markov gap.