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:2310.11242 · Physica Scripta

Odd entanglement entropy in boundary conformal field theories and holographic moving mirrors

Anjali Kumari, Vinayak Raj, Gautam Sengupta

Published Sep 10, 2026• 0 citations
arXivHTMLPDF

Abstract

Abstract We obtain the odd entanglement entropy (OEE) for bipartite mixed states in ( 1 + 1 ) -dimensional boundary conformal field theories (BCFT 2 s) utilizing an appropriate replica technique. For the generic configuration of two disjoint intervals, the large- c factorization of the twist field correlator leads to several distinct phases depending on the relative sizes and separations of the intervals. The resulting expressions match consistently with the entanglement wedge cross section (EWCS) for the bulk AdS 3 braneworld geometries, thereby extending the proposed holographic duality between the difference of the OEE and the entanglement entropy with the EWCS to BCFT setups. Furthermore, we obtain the OEE for these mixed states in related holographic moving mirror models which simulate Hawking radiation from black holes and verify the above duality in these time-dependent backgrounds. In this context we analyze the time evolution of the OEE and establish the analogues of Page curves for this mixed-state correlation measure.

DOI
10.1088/1402-4896/aea5a5

Related papers

Odd entanglement entropy in Galilean conformal field theories and flat holography

Jaydeep Kumar Basak, Himanshu Chourasiya, Vinayak Raj +1 more

Abstract The odd entanglement entropy (OEE) for bipartite states in a class of $$(1+1)$$ ( 1 + 1 ) -dimensional Galilean conformal field theories ( $$GCFT_{1+1}$$ G C F T 1 + 1 ) is obtained through an appropriate replica technique. In this context our results are compared with the entanglement wedge cross section (EWCS) for $$(2+1)$$ ( 2 + 1 ) -dimensional asymptotically flat geometries dual to the $$GCFT_{1+1}$$ G C F T 1 + 1 in the framework of flat holography. We find that our results are consistent with the duality of the difference between the odd entanglement entropy and the entanglement entropy of bipartite states, with the bulk EWCS for flat holographic scenarios.

arXiv:2203.03902•The European Physical Journal C•Nov 20, 2022•5 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

Odd entanglement entropy in TT¯ deformed CFT2s and holography

Debarshi Basu, Saikat Biswas, Ankur Dey +2 more

We construct a replica technique to perturbatively compute the odd entanglement entropy (OEE) for bipartite mixed states in $\mathrm{T}\overline{\mathrm{T}}$ deformed ${\mathrm{CFT}}_{2}\mathrm{s}$. This framework is then utilized to obtain the leading-order correction to the OEE for two disjoint intervals, two adjacent intervals, and a single interval in $\mathrm{T}\overline{\mathrm{T}}$ deformed thermal ${\mathrm{CFT}}_{2}\mathrm{s}$ in the large central charge limit. The field theory results are subsequently reproduced in the high-temperature limit from holographic computations for the entanglement wedge cross sections in the dual bulk finite cutoff Ba\~nados-Teitelboim-Zanelli geometries. We further show that for finite size $\mathrm{T}\overline{\mathrm{T}}$ deformed ${\mathrm{CFT}}_{2}\mathrm{s}$ at zero temperature the corrections to the OEE are vanishing to the leading order from both field theory and bulk holographic computations.

arXiv:2307.04832•Physical review. D/Physical review. D.•Dec 15, 2023•8 citations

Reflected entropy and entanglement negativity for holographic moving mirrors

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

Abstract We investigate the time evolution of reflected entropy and entanglement negativity for mixed state configurations involving two adjacent and disjoint intervals in the radiation flux of moving mirrors by utilizing the AdS/BCFT duality. These measures are computed for the required mixed state configurations by using the respective replica techniques in the large central charge limit of the BCFT1+1. We demonstrate that the results obtained exactly agree with the corresponding holographic computations in the dual bulk AdS3 geometry with an end of the world brane. In this context, the analogues of the Page curves for these measures are obtained for the required configurations in the radiation flux of kink and escaping mirrors which mimic the Hawking radiation from evaporating and eternal black holes respectively.

arXiv:2204.06015•Journal of High Energy Physics•Sep 13, 2022•14 citations

Time-like entanglement entropy in AdS/BCFT

Chong‐Sun Chu, Himanshu Parihar

Abstract We study the entanglement entropy for time-like subsystem in two-dimensional boundary conformal field theory (BCFT) both from the field theory and holographic point of view. In field theory, we compute the time-like entanglement entropy of a pure time-like interval at zero and finite temperature using the replica technique and analytical continuation. We find that, similar to the ordinary space-like entanglement entropy in BCFT, the time-like entropy also has a bulk phase and a boundary phase which corresponds respectively to the dominance of the identity block in the bulk and boundary OPE channels. However, we find that in Lorentzian BCFT, the time-like entanglement entropy posses a third Regge phase which arises in the Regge limit of the interval, when one endpoint of the time interval approaches the light cone of the mirror image of the other endpoint. We determine the phase diagram for the time-like entanglement entropy. We find that while the time-like entropy is complex in the bulk phase and has a boundary term in the boundary phase, there is no boundary entropy in the Regge phase. Moreover, it can be real or complex depending on which side the Regge limit is approached from. On the gravity side, we obtain the holographic time-like entanglement entropy from the corresponding bulk dual geometries and find exact agreement with the field theory results. The time-like entanglement entropy may be useful to describe the entanglement of a quantum dot on a half line.

arXiv:2304.10907•Journal of High Energy Physics•Jun 26, 2023•33 citations

Reflected entropy in Galilean conformal field theories and flat holography

Jaydeep Kumar Basak, Himanshu Chourasiya, Vinayak Raj +1 more

Abstract We obtain the reflected entropy for bipartite states in a class of $$(1+1)$$ ( 1 + 1 ) -dimensional Galilean conformal field theories $$(GCFT_{1+1})$$ ( G C F T 1 + 1 ) through a replica technique. Furthermore we compare our results with the entanglement wedge cross section (EWCS) obtained for the dual (2 + 1) dimensional asymptotically flat geometries in the context of flat holography. We find that our results are consistent with the duality between the reflected entropy and the bulk EWCS for flat holographic scenarios.

arXiv:2202.01201•The European Physical Journal C•Dec 26, 2022•11 citations
Abstract We obtain the odd entanglement entropy (OEE) for bipartite mixed states in ( 1 + 1 ) -dimensional boundary conformal field theories (BCFT 2 s) utilizing an appropriate replica technique. For the generic configuration of two disjoint intervals, the large- c factorization of the twist field correlator leads to several distinct phases depending on the relative sizes and separations of the intervals. The resulting expressions match consistently with the entanglement wedge cross section (EWCS) for the bulk AdS 3 braneworld geometries, thereby extending the proposed holographic duality between the difference of the OEE and the entanglement entropy with the EWCS to BCFT setups. Furthermore, we obtain the OEE for these mixed states in related holographic moving mirror models which simulate Hawking radiation from black holes and verify the above duality in these time-dependent backgrounds. In this context we analyze the time evolution of the OEE and establish the analogues of Page curves for this mixed-state correlation measure.
Abstract The odd entanglement entropy (OEE) for bipartite states in a class of (1+1)(1+1)(1+1) ( 1 + 1 ) -dimensional Galilean conformal field theories ( GCFT1+1GCFT_{1+1}GCFT1+1​ G C F T 1 + 1 ) is obtained through an appropriate replica technique. In this context our results are compared with the entanglement wedge cross section (EWCS) for (2+1)(2+1)(2+1) ( 2 + 1 ) -dimensional asymptotically flat geometries dual to the GCFT1+1GCFT_{1+1}GCFT1+1​ G C F T 1 + 1 in the framework of flat holography. We find that our results are consistent with the duality of the difference between the odd entanglement entropy and the entanglement entropy of bipartite states, with the bulk EWCS for flat holographic scenarios.
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.
We construct a replica technique to perturbatively compute the odd entanglement entropy (OEE) for bipartite mixed states in TT‾\mathrm{T}\overline{\mathrm{T}}TT deformed CFT2s{\mathrm{CFT}}_{2}\mathrm{s}CFT2​s. This framework is then utilized to obtain the leading-order correction to the OEE for two disjoint intervals, two adjacent intervals, and a single interval in TT‾\mathrm{T}\overline{\mathrm{T}}TT deformed thermal CFT2s{\mathrm{CFT}}_{2}\mathrm{s}CFT2​s in the large central charge limit. The field theory results are subsequently reproduced in the high-temperature limit from holographic computations for the entanglement wedge cross sections in the dual bulk finite cutoff Ba\~nados-Teitelboim-Zanelli geometries. We further show that for finite size TT‾\mathrm{T}\overline{\mathrm{T}}TT deformed CFT2s{\mathrm{CFT}}_{2}\mathrm{s}CFT2​s at zero temperature the corrections to the OEE are vanishing to the leading order from both field theory and bulk holographic computations.
Abstract We investigate the time evolution of reflected entropy and entanglement negativity for mixed state configurations involving two adjacent and disjoint intervals in the radiation flux of moving mirrors by utilizing the AdS/BCFT duality. These measures are computed for the required mixed state configurations by using the respective replica techniques in the large central charge limit of the BCFT1+1. We demonstrate that the results obtained exactly agree with the corresponding holographic computations in the dual bulk AdS3 geometry with an end of the world brane. In this context, the analogues of the Page curves for these measures are obtained for the required configurations in the radiation flux of kink and escaping mirrors which mimic the Hawking radiation from evaporating and eternal black holes respectively.
Abstract We study the entanglement entropy for time-like subsystem in two-dimensional boundary conformal field theory (BCFT) both from the field theory and holographic point of view. In field theory, we compute the time-like entanglement entropy of a pure time-like interval at zero and finite temperature using the replica technique and analytical continuation. We find that, similar to the ordinary space-like entanglement entropy in BCFT, the time-like entropy also has a bulk phase and a boundary phase which corresponds respectively to the dominance of the identity block in the bulk and boundary OPE channels. However, we find that in Lorentzian BCFT, the time-like entanglement entropy posses a third Regge phase which arises in the Regge limit of the interval, when one endpoint of the time interval approaches the light cone of the mirror image of the other endpoint. We determine the phase diagram for the time-like entanglement entropy. We find that while the time-like entropy is complex in the bulk phase and has a boundary term in the boundary phase, there is no boundary entropy in the Regge phase. Moreover, it can be real or complex depending on which side the Regge limit is approached from. On the gravity side, we obtain the holographic time-like entanglement entropy from the corresponding bulk dual geometries and find exact agreement with the field theory results. The time-like entanglement entropy may be useful to describe the entanglement of a quantum dot on a half line.
Abstract We obtain the reflected entropy for bipartite states in a class of (1+1)(1+1)(1+1) ( 1 + 1 ) -dimensional Galilean conformal field theories (GCFT1+1)(GCFT_{1+1})(GCFT1+1​) ( G C F T 1 + 1 ) through a replica technique. Furthermore we compare our results with the entanglement wedge cross section (EWCS) obtained for the dual (2 + 1) dimensional asymptotically flat geometries in the context of flat holography. We find that our results are consistent with the duality between the reflected entropy and the bulk EWCS for flat holographic scenarios.