Holographic inequalities and entanglement of purification

Bao, Ning; Halpern, Illan F.

doi:10.1007/jhep03(2018)006

Cited by 72 publications

(81 citation statements)

References 28 publications

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“…Even boundary-anchored surfaces can already reach past event horizons, as in the case of Vaidya spacetimes, so it is natural to ask just how far these bulk-anchored surfaces reach. Furthermore, it would be interesting to ask how multipartite and conditional entanglements of purification [84][85][86] can also help to probe deeper into the bulk.…”

Section: Going Deeper?mentioning

confidence: 99%

Towards bulk metric reconstruction from extremal area variations

Bao

Cao

Fischetti

et al. 2019

Class. Quantum Grav.

Self Cite

105

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The Ryu-Takayanagi and Hubeny-Rangamani-Takayanagi formulae suggest that bulk geometry emerges from the entanglement structure of the boundary theory. Using these formulae, we build on a result of Alexakis, Balehowsky, and Nachman to show that in four bulk dimensions, the entanglement entropies of boundary regions of disk topology uniquely fix the bulk metric in any region foliated by the corresponding HRT surfaces. More generally, for a bulk of any dimension d ≥ 4, knowledge of the (variations of the) areas of two-dimensional boundary-anchored extremal surfaces of disk topology uniquely fixes the bulk metric wherever these surfaces reach. This result is covariant and not reliant on any symmetry assumptions; its applicability thus includes regions of strong dynamical gravity such as the early-time interior of black holes formed from collapse. While we only show uniqueness of the metric, the approach we present provides a clear path towards an explicit spacetime metric reconstruction.

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Section: Going Deeper?mentioning

confidence: 99%

Towards bulk metric reconstruction from extremal area variations

Bao

Cao

Fischetti

et al. 2019

Class. Quantum Grav.

Self Cite

105

View full text Add to dashboard Cite

show abstract

“…Another future direction is to extend the analysis of this paper to other measures of entanglement for which holographic recipes have been proposed, of which a recent example is the entanglement of purification [33][34][35].…”

Section: Jhep06(2018)130mentioning

confidence: 99%

Gravity from entanglement for boundary subregions

Blanco

Leston

Pérez-Nadal

2018

J. High Energ. Phys.

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Abstract:We explore several aspects of the relation between gravity and entanglement in the context of AdS/CFT, in the simple setting of 3 bulk dimensions. Specifically, we consider small perturbations of the AdS metric and the CFT vacuum state and study what can be learnt about the metric perturbation from the Ryu-Takayanagi (RT) formula alone. It is well-known that, if the RT formula holds for all boundary spacelike segments, then the metric perturbation satisfies the linearized Einstein equations throughout the bulk. We generalize this result by showing that, if the RT formula holds for all spacelike segments contained in a certain boundary region, then the metric perturbation satisfies the linearized Einstein equations in a corresponding bulk region (in fact, it is completely determined in that region). We also argue that the same is true for small perturbations of the planar BTZ black hole and the CFT thermal state. We discuss the relation between our results and the ideas of subregion-subregion duality, and we point out that our argument also serves as a holographic proof of the linearized RT formula for boundary segments.

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“…Also using a generalization of the above proposal to time dependent backgrounds, [14,21] studied the evolution of EoP after a quantum quench in the dual field theory. Related investigations attempting to better understand EoP both in the field theory and holography have also appeared in [22][23][24][25][26][27][28][29][30][31][32].…”

Section: Introductionmentioning

confidence: 99%

Some aspects of entanglement wedge cross-section

Velni

Mozaffar

Vahidinia

2019

J. High Energ. Phys.

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We consider the minimal area of the entanglement wedge cross section (EWCS) in Einstein gravity. In the context of holography, it is proposed that this quantity is dual to different information measures, e.g., entanglement of purification, logarithmic negativity and reflected entropy. Motivated by these proposals, we examine in detail the low and high temperature corrections to this quantity and show that it obeys the area law even in the finite temperature. We also study EWCS in nonrelativistic field theories with nontrivial Lifshitz and hyperscaling violating exponents. The resultant EWCS is an increasing function of the dynamical exponent due to the enhancement of spatial correlations between subregions for larger values of z. We find that EWCS is monotonically decreasing as the hyperscaling violating exponent increases. We also obtain this quantity for an entangling region with singular boundary in a three dimensional field theory and find a universal contribution where the coefficient depends on the central charge. Finally, we verify that for higher dimensional singular regions the corresponding EWCS obeys the area law.where G N is the Newton constant and Γ A is a codimension-2, spacelike minimal hypersurface in the bulk spacetime, anchored to the asymptotic boundary such that ∂Γ A = ∂A (see figure 1). The RT proposal which passes a variety of consistency tests, generalizes to time dependent case [2] and higher derivative theories of gravity [3][4][5][6]. Using these prescriptions, the correlation of several disconnected components can also be considered. In particular when the entangling region is made by two disjoint spatial components, an important quantity to study is the holographic mutual

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Holographic inequalities and entanglement of purification

Cited by 72 publications

References 28 publications

Towards bulk metric reconstruction from extremal area variations

Towards bulk metric reconstruction from extremal area variations

Gravity from entanglement for boundary subregions

Some aspects of entanglement wedge cross-section

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