Aspects of the Papadodimas-Raju proposal for the black hole interior

Harlow, Daniel

doi:10.1007/jhep11(2014)055

Cited by 60 publications

(118 citation statements)

References 107 publications

(316 reference statements)

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“…we do not discuss black hole interiors and we are not violating quantum mechanics [16]. A connection between black holes and quantum error correction was also made in [17], which is essentially an earlier version of the proposal of [15], but again the context was different and our work here should be uncontroversial by comparison.…”

Section: Jhep04(2015)163mentioning

confidence: 92%

“…Let us first see that this ensures we can correct the erasure. The Schmidt decomposition 7 of |φ , together with (3.14), ensures us that there exists a basis |e for E and a set of orthonormal states |ψ i,e E in E such that 16) where C e are some non-negative coefficients obeying e C 2 e = 1. In other words there exists a unitary transformation U E acting only on E such that…”

Section: General Erasure Correctionmentioning

confidence: 99%

“…16 In the figure, the intersection of the entanglement wedge with a bulk Cauchy surface 16 One argument that this must be the case is as follows: the extension by [37] of the Ryu-Takayanagi proposal [38] to next to leading order in 1/N claims that bulk entanglement entropy in the entanglement wedge contributes to the Von Neumann entropy SA. So for example if we have a spin sitting in the entanglement wedge of A that is entangled with another spin in WC [A], then the spin in the entanglement JHEP04 (2015)163 is shaded blue; the minimal area condition causes a discontinuous change as we increase the size of A.…”

Section: Disconnected Regions and Quantum Secret Sharingmentioning

confidence: 99%

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Bulk locality and quantum error correction in AdS/CFT

Almheiri

Dong

Harlow

2015

J. High Energ. Phys.

Self Cite

704

1,132

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We point out a connection between the emergence of bulk locality in AdS/CFT and the theory of quantum error correction. Bulk notions such as Bogoliubov transformations, location in the radial direction, and the holographic entropy bound all have natural CFT interpretations in the language of quantum error correction. We also show that the question of whether bulk operator reconstruction works only in the causal wedge or all the way to the extremal surface is related to the question of whether or not the quantum error correcting code realized by AdS/CFT is also a "quantum secret sharing scheme", and suggest a tensor network calculation that may settle the issue. Interestingly, the version of quantum error correction which is best suited to our analysis is the somewhat nonstandard "operator algebra quantum error correction" of Beny, Kempf, and Kribs. Our proposal gives a precise formulation of the idea of "subregion-subregion" duality in AdS/CFT, and clarifies the limits of its validity.

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Section: Jhep04(2015)163mentioning

confidence: 92%

Section: General Erasure Correctionmentioning

confidence: 99%

Section: Disconnected Regions and Quantum Secret Sharingmentioning

confidence: 99%

See 1 more Smart Citation

Bulk locality and quantum error correction in AdS/CFT

Almheiri

Dong

Harlow

2015

J. High Energ. Phys.

Self Cite

704

1,132

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show abstract

“…Such problems remain extremely perplexing and important, but they are difficult (or impossible?) to formulate as a precise question about CFT observables, and progress on this front may require qualitatively new 'observables' [19][20][21].…”

Section: The Information Paradox and The Vacuum Blockmentioning

confidence: 99%

Conformal blocks beyond the semi-classical limit

Fitzpatrick

Kaplan

2016

J. High Energ. Phys.

149

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Black hole microstates and their approximate thermodynamic properties can be studied using heavy-light correlation functions in AdS/CFT. Universal features of these correlators can be extracted from the Virasoro conformal blocks in CFT 2 , which encapsulate quantum gravitational effects in AdS 3 . At infinite central charge c, the Virasoro vacuum block provides an avatar of the black hole information paradox in the form of periodic Euclidean-time singularities that must be resolved at finite c.We compute Virasoro blocks in the heavy-light, large c limit, extending our previous results by determining perturbative 1/c corrections. We obtain explicit closed-form expressions for both the 'semi-classical' h 2 L /c 2 and 'quantum' h L /c 2 corrections to the vacuum block, and we provide integral formulas for general Virasoro blocks. We comment on the interpretation of our results for thermodynamics, discussing how monodromies in Euclidean time can arise from AdS calculations using 'geodesic Witten diagrams'. We expect that only non-perturbative corrections in 1/c can resolve the singularities associated with the information paradox.

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“…2 One may argue that φ( y) does correspond to a gauge-invariant bulk operator if we work in radial gauge, since then φ( y) =φ( y) for a Wilson line that stretches along the radial direction. However, as we will explain, radial gauge is disallowed in the eternal black hole background, which is why we considerφ (see also [18]). 3 Other framings are also possible (including smeared ones as e.g.…”

Section: Introductionmentioning

confidence: 99%

On the construction of charged operators inside an eternal black hole

Guica

Jafferis

2017

SciPost Phys.

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We revisit the holographic construction of (approximately) local bulk operators inside an eternal AdS black hole in terms of operators in the boundary CFTs. If the bulk operator carries charge, the construction must involve a qualitatively new object: a Wilson line that stretches between the two boundaries of the eternal black hole. This operatormore precisely, its zero mode -cannot be expressed in terms of the boundary currents and only exists in entangled states dual to two-sided geometries, which suggests that it is a state-dependent operator. We determine the action of the Wilson line on the relevant subspaces of the total Hilbert space, and show that it behaves as a local operator from the point of view of either CFT. For the case of three bulk dimensions, we give explicit expressions for the charged bulk field and the Wilson line. Furthermore, we show that when acting on the thermofield double state, the Wilson line may be extracted from a limit of certain standard CFT operator expressions. We also comment on the relationship between the Wilson line and previously discussed mirror operators in the eternal black hole.

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Aspects of the Papadodimas-Raju proposal for the black hole interior

Cited by 60 publications

References 107 publications

Bulk locality and quantum error correction in AdS/CFT

Bulk locality and quantum error correction in AdS/CFT

Conformal blocks beyond the semi-classical limit

On the construction of charged operators inside an eternal black hole

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