Connecting Fisher information to bulk entanglement in holography

Banerjee, Souvik; Erdmenger, Johanna; Sarkar, Debajyoti

doi:10.1007/jhep08(2018)001

Cited by 68 publications

(95 citation statements)

References 56 publications

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“…In this case it is known that the corresponding fidelity susceptibility is indeed the heat capacity. It is then illustrative to study this case in our framework (see also [14,15]). …”

Section: Discussionmentioning

confidence: 99%

Holographic fidelity susceptibility

Alishahiha

Astaneh

2017

Phys. Rev. D

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For a field theory with a gravitational dual, we study holographic fidelity susceptibility for two states related by a deformation of a relevant operator. To do so, we study back reaction of a massive scalar field on the asymptotic behavior of the metric in an Einstein gravity coupled to a massive scalar field. Identifying the two states, holographically, with the original and back reacted geometries, the corresponding holographic fidelity susceptibility is given by the difference of the volume of an extremal time slice evaluated on the original and back reacted geometries.

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“…In this case it is known that the corresponding fidelity susceptibility is indeed the heat capacity. It is then illustrative to study this case in our framework (see also [14,15]). …”

Section: Discussionmentioning

confidence: 99%

Holographic fidelity susceptibility

Alishahiha

Astaneh

2017

Phys. Rev. D

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“…In this section we will find an expression for the fidelity of these two states. The fidelity of holographic states has previously been considered in [60][61][62] and others.…”

Section: Fidelity From a Replica Trickmentioning

confidence: 99%

The holographic dual of the entanglement wedge symplectic form

Kirklin

2020

J. High Energ. Phys.

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In this paper, we find the boundary dual of the symplectic form for the bulk fields in any entanglement wedge. The key ingredient is Uhlmann holonomy, which is a notion of parallel transport of purifications of density matrices based on a maximisation of transition probabilities. Using a replica trick, we compute this holonomy for curves of reduced states in boundary subregions of holographic QFTs at large N , subject to changes of operator insertions on the boundary. It is shown that the Berry phase along Uhlmann parallel paths may be written as the integral of an abelian connection whose curvature is the symplectic form of the entanglement wedge. This generalises previous work on holographic Berry curvature.

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“…While the area of the Ryu‐Takayanagi (RT) surface

γ_{R T}

of A is known to give the entanglement entropy of A , it was proposed in [] that the subregion complexity should correspond to the volume of the co‐dimension 1 region Σ enclosed by

γ_{R T}

and the cutoff surface ( Figure ). Other recent proposals relate bulk volumes to Fisher information and fidelity susceptibility …”

Section: Introductionmentioning

confidence: 99%

Topological Complexity in AdS₃/CFT₂

Abt

Erdmenger

Hinrichsen

et al. 2018

Fortschritte der Physik

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106

123

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We consider subregion complexity within the AdS3/CFT2 correspondence. We rewrite the volume proposal, according to which the complexity of a reduced density matrix is given by the spacetime volume contained inside the associated Ryu‐Takayanagi (RT) surface, in terms of an integral over the curvature. Using the Gauss‐Bonnet theorem we evaluate this quantity for general entangling regions and temperature. In particular, we find that the discontinuity that occurs under a change in the RT surface is given by a fixed topological contribution, independent of the temperature or details of the entangling region. We offer a definition and interpretation of subregion complexity in the context of tensor networks, and show numerically that it reproduces the qualitative features of the holographic computation in the case of a random tensor network using its relation to the Ising model. Finally, we give a prescription for computing subregion complexity directly in CFT using the kinematic space formalism, and use it to reproduce some of our explicit gravity results obtained at zero temperature. We thus obtain a concrete matching of results for subregion complexity between the gravity and tensor network approaches, as well as a CFT prescription.

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Connecting Fisher information to bulk entanglement in holography

Cited by 68 publications

References 56 publications

Holographic fidelity susceptibility

Holographic fidelity susceptibility

The holographic dual of the entanglement wedge symplectic form

Topological Complexity in AdS₃/CFT₂

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Connecting Fisher information to bulk entanglement in holography

Cited by 68 publications

References 56 publications

Holographic fidelity susceptibility

Holographic fidelity susceptibility

The holographic dual of the entanglement wedge symplectic form

Topological Complexity in AdS3/CFT2

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Topological Complexity in AdS₃/CFT₂