Reconstruction of Bulk Operators within the Entanglement Wedge in Gauge-Gravity Duality

Dong, Xi; Harlow, Daniel; Wall, Aron C.

doi:10.1103/physrevlett.117.021601

Cited by 464 publications

(710 citation statements)

References 60 publications

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“…The importance of this condition was recently emphasized in [18], who phrased it as the requirement of hermiticity. In particular, they proved that in order to satisfy (4.12), the field Φ must lie within the bulk entanglement wedge of the boundary region that contains the operator O.…”

Section: Jhep04(2016)119mentioning

confidence: 99%

Precursors, gauge invariance, and quantum error correction in AdS/CFT

Freivogel

Jefferson

Kabir

2016

J. High Energ. Phys.

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A puzzling aspect of the AdS/CFT correspondence is that a single bulk operator can be mapped to multiple different boundary operators, or precursors. By improving upon a recent model of Mintun, Polchinski, and Rosenhaus, we demonstrate explicitly how this ambiguity arises in a simple model of the field theory. In particular, we show how gauge invariance in the boundary theory manifests as a freedom in the smearing function used in the bulk-boundary mapping, and explicitly show how this freedom can be used to localize the precursor in different spatial regions. We also show how the ambiguity can be understood in terms of quantum error correction, by appealing to the entanglement present in the CFT. The concordance of these two approaches suggests that gauge invariance and entanglement in the boundary field theory are intimately connected to the reconstruction of local operators in the dual spacetime.

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Section: Jhep04(2016)119mentioning

confidence: 99%

Precursors, gauge invariance, and quantum error correction in AdS/CFT

Freivogel

Jefferson

Kabir

2016

J. High Energ. Phys.

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“…This connection between correctability and geometry is encapsulated by the entanglement wedge hypothesis [17][18][19][20], which holds in AdS=CFT [21,22]. This hypothesis specifies the largest bulk region whose logical subalgebra can be represented on a given boundary region.…”

Section: A Entanglement Wedge Reconstructionmentioning

confidence: 99%

Code Properties from Holographic Geometries

2017

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Almheiri, Dong, and Harlow [J. High Energy Phys. 04 (2015) 163.] proposed a highly illuminating connection between the AdS=CFT holographic correspondence and operator algebra quantum error correction (OAQEC). Here, we explore this connection further. We derive some general results about OAQEC, as well as results that apply specifically to quantum codes that admit a holographic interpretation. We introduce a new quantity called price, which characterizes the support of a protected logical system, and find constraints on the price and the distance for logical subalgebras of quantum codes. We show that holographic codes defined on bulk manifolds with asymptotically negative curvature exhibit uberholography, meaning that a bulk logical algebra can be supported on a boundary region with a fractal structure. We argue that, for holographic codes defined on bulk manifolds with asymptotically flat or positive curvature, the boundary physics must be highly nonlocal, an observation with potential implications for black holes and for quantum gravity in AdS space at distance scales that are small compared to the AdS curvature radius.

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“…To remedy the problem, we explore the 1 Interested readers are referred to [13,14] for a comprehensive review on tensor networks and its diverse applications in various branches of theoretical physics. Also we list out some references [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30] where the connection between reconstruction of bulk spacetime and entanglement in the context of holography have been explored. This list is by no means complete and the readers are encouraged to check the citations of these papers and the references within.…”

Section: Jhep08(2016)086 1 Introductionmentioning

confidence: 99%

Exploring the tensor networks/AdS correspondence

Bhattacharyya

Gao

Hung

et al. 2016

J. High Energ. Phys.

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In this paper we study the recently proposed tensor networks/AdS correspondence. We found that the Coxeter group is a useful tool to describe tensor networks in a negatively curved space. Studying generic tensor network populated by perfect tensors, we find that the physical wave function generically do not admit any connected correlation functions of local operators. To remedy the problem, we assume that wavefunctions admitting such semi-classical gravitational interpretation are composed of tensors close to, but not exactly perfect tensors. Computing corrections to the connected two point correlation functions, we find that the leading contribution is given by structures related to geodesics connecting the operators inserted at the boundary physical dofs. Such considerations admit generalizations at least to three point functions. This is highly suggestive of the emergence of the analogues of Witten diagrams in the tensor network. The perturbations alone however do not give the right entanglement spectrum. Using the Coxeter construction, we also constructed the tensor network counterpart of the BTZ black hole, by orbifolding the discrete lattice on which the network resides. We found that the construction naturally reproduces some of the salient features of the BTZ black hole, such as the appearance of RT surfaces that could wrap the horizon, depending on the size of the entanglement region A.

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Reconstruction of Bulk Operators within the Entanglement Wedge in Gauge-Gravity Duality

Cited by 464 publications

References 60 publications

Precursors, gauge invariance, and quantum error correction in AdS/CFT

Precursors, gauge invariance, and quantum error correction in AdS/CFT

Code Properties from Holographic Geometries

Exploring the tensor networks/AdS correspondence

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