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:1908.09939 · Physical Review Letters

Entanglement Wedges from the Information Metric in Conformal Field Theories

Yu-ki Suzuki, Tadashi Takayanagi, Koji Umemoto

Published Nov 26, 2019• 36 citations
arXivHTMLPDF

Abstract

We present a new method of deriving the geometry of entanglement wedges in holography directly from conformal field theories (CFTs). We analyze an information metric called the Bures metric of reduced density matrices for locally excited states. This measures the distinguishability of states with different points excited. For a subsystem given by an interval, we precisely reproduce the expected entanglement wedge for two-dimensional holographic CFTs from the Bures metric, which turns out to be proportional to the anti-de Sitter metric on a time slice. On the other hand, for free scalar CFTs, we do not find any sharp structures like entanglement wedges. When a subsystem consists of two disconnected intervals, we manage to reproduce the expected entanglement wedge from holographic CFTs with the correct phase transitions, up to a very small error, from a quantity alternative to the Bures metric.

DOI
10.1103/physrevlett.123.221601

Related papers

Looking at shadows of entanglement wedges

Yuya Kusuki, Yu-ki Suzuki, Tadashi Takayanagi +1 more

We present a new method of deriving shapes of entanglement wedges directly from conformal field theory (CFT) calculations. We point out that a reduced density matrix in holographic CFTs possesses a sharp wedge structure such that inside the wedge we can distinguish two local excitations, while outside we cannot. We can determine this wedge, which we call a CFT wedge, by computing a distinguishability measure. We find that CFT wedges defined by the fidelity or Bures distance as a distinguishability measure coincide perfectly with shadows of entanglement wedges in anti-de Sitter (AdS)/CFT. We confirm this agreement between CFT wedges and entanglement wedges for two-dimensional holographic CFTs where the subsystem is chosen to be an interval or double intervals, as well as higher-dimensional CFTs with a round ball subsystem. On the other hand, if we consider a free scalar CFT, we find that there are no sharp CFT wedges. This shows that sharp entanglement wedges emerge only for holographic CFTs owing to the large-N factorization. We also generalize our analysis to a time-dependent example and to a holographic boundary conformal field theory (AdS/BCFT). Finally, we study other distinguishability measures to define CFT wedges. We observe that some of the measures lead to CFT wedges which slightly deviate from the entanglement wedges in AdS/CFT, and we give a heuristic explanation for this. This paper is an extended version of our earlier letter (arXiv:1908.09939 [hep-th]) and includes various new observations and examples.

•Nov 1, 2020•34 citations

Looking at shadows of entanglement wedges

Yuya Kusuki, Yuki Suzuki, Tadashi Takayanagi +1 more

Abstract We present a new method of deriving shapes of entanglement wedges directly from conformal field theory (CFT) calculations. We point out that a reduced density matrix in holographic CFTs possesses a sharp wedge structure such that inside the wedge we can distinguish two local excitations, while outside we cannot. We can determine this wedge, which we call a CFT wedge, by computing a distinguishability measure. We find that CFT wedges defined by the fidelity or Bures distance as a distinguishability measure coincide perfectly with shadows of entanglement wedges in anti-de Sitter (AdS)/CFT. We confirm this agreement between CFT wedges and entanglement wedges for two-dimensional holographic CFTs where the subsystem is chosen to be an interval or double intervals, as well as higher-dimensional CFTs with a round ball subsystem. On the other hand, if we consider a free scalar CFT, we find that there are no sharp CFT wedges. This shows that sharp entanglement wedges emerge only for holographic CFTs owing to the large-$N$ factorization. We also generalize our analysis to a time-dependent example and to a holographic boundary conformal field theory (AdS/BCFT). Finally, we study other distinguishability measures to define CFT wedges. We observe that some of the measures lead to CFT wedges which slightly deviate from the entanglement wedges in AdS/CFT, and we give a heuristic explanation for this. This paper is an extended version of our earlier letter (arXiv:1908.09939 [hep-th]) and includes various new observations and examples.

arXiv:1912.08423•Progress of Theoretical and Experimental Physics•Oct 7, 2020•22 citations

Entanglement Wedge Cross Section from the Dual Density Matrix

Kotaro Tamaoka

We define a new information theoretic quantity called odd entanglement entropy (OEE) which enables us to compute the entanglement wedge cross section in holographic conformal field theories (CFTs). The entanglement wedge cross section has been introduced as a minimal cross section of the entanglement wedge, a natural generalization of the Ryu-Takayanagi surface. By using the replica trick, we explicitly compute the OEE for two-dimensional holographic CFT (three-dimensional anti-de Sitter space and planar Bañados-Teitelboim-Zanelli black hole) and see agreement with the entanglement wedge cross section. We conjecture this relation will hold in general dimensions.

arXiv:1809.09109•Physical Review Letters•Apr 9, 2019•157 citations

Entanglement Asymmetry in Conformal Field Theory and Holography

Francesco Benini, Victor Godet, Amartya Harsh Singh

Abstract Entanglement asymmetry is a measure of symmetry breaking in quantum subsystems, inspired by quantum information theory, particularly suited to study out-of-equilibrium states. We study the entanglement asymmetry of a class of excited “coherent states” in conformal quantum field theories with a U(1) symmetry, employing Euclidean path-integral methods with topological symmetry defects and the replica formalism. We compute, at leading order in perturbation theory, the asymmetry for a variety of subsystems, including finite spherical subregions in flat space, in finite volume, and at positive temperature. We also study its Lorentzian time evolution, showcasing the dynamical restoration of the symmetry due to thermalization, as well as the presence of a quantum Mpemba effect. Our results are universal, and apply in any number of dimensions. We also show that the perturbative entanglement asymmetry is related to the Fisher information metric, which has a known holographic dual called the Hollands–Wald canonical energy, and that it is captured by the anti-de-Sitter bulk charge contained in the entanglement wedge.

arXiv:2407.07969•Progress of Theoretical and Experimental Physics•May 21, 2025•21 citations

Holographic de Sitter Geometry from Entanglement in Conformal Field Theory

Jan De Boer A, Michał P. Heller, Robert Cobb Myers +1 more

We demonstrate that, for general conformal field theories (CFTs), the entanglement for small perturbations of the vacuum is organized in a novel holographic way. For spherical entangling regions in a constant time slice, perturbations in the entanglement entropy are solutions of a Klein-Gordon equation in an auxiliary de Sitter (dS) spacetime. The role of the emergent timelike direction in dS spacetime is played by the size of the entangling sphere. For CFTs with extra conserved charges, e.g., higher-spin charges, we show that each charge gives rise to a separate dynamical scalar field in dS spacetime.

arXiv:1509.00113•Physical Review Letters•Feb 10, 2016•52 citations

Entanglement wedge in flat holography and entanglement negativity

Debarshi Basu, Ashish Chandra, Vinayak Raj +1 more

We establish a construction for the entanglement wedge in asymptotically flat bulk geometries for subsystems in dual (1+1)-dimensional Galilean conformal field theories in the context of flat space holography. In this connection we propose a definition for the bulk entanglement wedge cross section for bipartite states of such dual non relativistic conformal field theories. Utilizing our construction for the entanglement wedge cross section we compute the entanglement negativity for such bipartite states through the generalization of an earlier proposal, in the context of the usual AdS/CFT scenario, to flat space holography. The entanglement negativity obtained from our construction exactly reproduces earlier holographic results and match with the corresponding field theory replica technique results in the large central charge limit.

arXiv:2106.14896•SciPost Physics Core•Mar 15, 2022•41 citations
We present a new method of deriving the geometry of entanglement wedges in holography directly from conformal field theories (CFTs). We analyze an information metric called the Bures metric of reduced density matrices for locally excited states. This measures the distinguishability of states with different points excited. For a subsystem given by an interval, we precisely reproduce the expected entanglement wedge for two-dimensional holographic CFTs from the Bures metric, which turns out to be proportional to the anti-de Sitter metric on a time slice. On the other hand, for free scalar CFTs, we do not find any sharp structures like entanglement wedges. When a subsystem consists of two disconnected intervals, we manage to reproduce the expected entanglement wedge from holographic CFTs with the correct phase transitions, up to a very small error, from a quantity alternative to the Bures metric.
We present a new method of deriving shapes of entanglement wedges directly from conformal field theory (CFT) calculations. We point out that a reduced density matrix in holographic CFTs possesses a sharp wedge structure such that inside the wedge we can distinguish two local excitations, while outside we cannot. We can determine this wedge, which we call a CFT wedge, by computing a distinguishability measure. We find that CFT wedges defined by the fidelity or Bures distance as a distinguishability measure coincide perfectly with shadows of entanglement wedges in anti-de Sitter (AdS)/CFT. We confirm this agreement between CFT wedges and entanglement wedges for two-dimensional holographic CFTs where the subsystem is chosen to be an interval or double intervals, as well as higher-dimensional CFTs with a round ball subsystem. On the other hand, if we consider a free scalar CFT, we find that there are no sharp CFT wedges. This shows that sharp entanglement wedges emerge only for holographic CFTs owing to the large-N factorization. We also generalize our analysis to a time-dependent example and to a holographic boundary conformal field theory (AdS/BCFT). Finally, we study other distinguishability measures to define CFT wedges. We observe that some of the measures lead to CFT wedges which slightly deviate from the entanglement wedges in AdS/CFT, and we give a heuristic explanation for this. This paper is an extended version of our earlier letter (arXiv:1908.09939 [hep-th]) and includes various new observations and examples.
Abstract We present a new method of deriving shapes of entanglement wedges directly from conformal field theory (CFT) calculations. We point out that a reduced density matrix in holographic CFTs possesses a sharp wedge structure such that inside the wedge we can distinguish two local excitations, while outside we cannot. We can determine this wedge, which we call a CFT wedge, by computing a distinguishability measure. We find that CFT wedges defined by the fidelity or Bures distance as a distinguishability measure coincide perfectly with shadows of entanglement wedges in anti-de Sitter (AdS)/CFT. We confirm this agreement between CFT wedges and entanglement wedges for two-dimensional holographic CFTs where the subsystem is chosen to be an interval or double intervals, as well as higher-dimensional CFTs with a round ball subsystem. On the other hand, if we consider a free scalar CFT, we find that there are no sharp CFT wedges. This shows that sharp entanglement wedges emerge only for holographic CFTs owing to the large-NNN factorization. We also generalize our analysis to a time-dependent example and to a holographic boundary conformal field theory (AdS/BCFT). Finally, we study other distinguishability measures to define CFT wedges. We observe that some of the measures lead to CFT wedges which slightly deviate from the entanglement wedges in AdS/CFT, and we give a heuristic explanation for this. This paper is an extended version of our earlier letter (arXiv:1908.09939 [hep-th]) and includes various new observations and examples.
We define a new information theoretic quantity called odd entanglement entropy (OEE) which enables us to compute the entanglement wedge cross section in holographic conformal field theories (CFTs). The entanglement wedge cross section has been introduced as a minimal cross section of the entanglement wedge, a natural generalization of the Ryu-Takayanagi surface. By using the replica trick, we explicitly compute the OEE for two-dimensional holographic CFT (three-dimensional anti-de Sitter space and planar Bañados-Teitelboim-Zanelli black hole) and see agreement with the entanglement wedge cross section. We conjecture this relation will hold in general dimensions.
Abstract Entanglement asymmetry is a measure of symmetry breaking in quantum subsystems, inspired by quantum information theory, particularly suited to study out-of-equilibrium states. We study the entanglement asymmetry of a class of excited “coherent states” in conformal quantum field theories with a U(1) symmetry, employing Euclidean path-integral methods with topological symmetry defects and the replica formalism. We compute, at leading order in perturbation theory, the asymmetry for a variety of subsystems, including finite spherical subregions in flat space, in finite volume, and at positive temperature. We also study its Lorentzian time evolution, showcasing the dynamical restoration of the symmetry due to thermalization, as well as the presence of a quantum Mpemba effect. Our results are universal, and apply in any number of dimensions. We also show that the perturbative entanglement asymmetry is related to the Fisher information metric, which has a known holographic dual called the Hollands–Wald canonical energy, and that it is captured by the anti-de-Sitter bulk charge contained in the entanglement wedge.
We demonstrate that, for general conformal field theories (CFTs), the entanglement for small perturbations of the vacuum is organized in a novel holographic way. For spherical entangling regions in a constant time slice, perturbations in the entanglement entropy are solutions of a Klein-Gordon equation in an auxiliary de Sitter (dS) spacetime. The role of the emergent timelike direction in dS spacetime is played by the size of the entangling sphere. For CFTs with extra conserved charges, e.g., higher-spin charges, we show that each charge gives rise to a separate dynamical scalar field in dS spacetime.
We establish a construction for the entanglement wedge in asymptotically flat bulk geometries for subsystems in dual (1+1)-dimensional Galilean conformal field theories in the context of flat space holography. In this connection we propose a definition for the bulk entanglement wedge cross section for bipartite states of such dual non relativistic conformal field theories. Utilizing our construction for the entanglement wedge cross section we compute the entanglement negativity for such bipartite states through the generalization of an earlier proposal, in the context of the usual AdS/CFT scenario, to flat space holography. The entanglement negativity obtained from our construction exactly reproduces earlier holographic results and match with the corresponding field theory replica technique results in the large central charge limit.