Relative entropy equals bulk relative entropy

By D. Jafferis, Aitor Lewkowycz, J. Maldacena, S. Suh. 2015

523 citations recorded by the source corpus.

A bstractWe consider the gravity dual of the modular Hamiltonian associated to a general subregion of a boundary theory. We use it to argue that the relative entropy of nearby states is given by the relative entropy in the bulk, to leading order in the bulk gravitational coupling. We also argue that the boundary modular flow is dual to the bulk modular flow in the entanglement wedge, with implications for entanglement wedge reconstruction.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/ec5dc4b77d9339838821c4e93b5e7284c5611a3d

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

1. D. Harlow
2. D. Stanford
3. R. Myers
4. S. Raju
5. J. Maldacena
6. S. Shenker
7. V. Hubeny
8. T. Faulkner

In Nuclear and High Energy Physics

1. D. Harlow
2. D. Stanford
3. R. Myers
4. S. Raju
5. J. Maldacena
6. S. Shenker
7. T. Faulkner
8. Thomas Hartman

In Statistical and Nonlinear Physics

1. D. Harlow
2. D. Stanford
3. S. Raju
4. R. Myers
5. S. Shenker
6. J. Maldacena
7. Henry Maxfield
8. T. Faulkner

Citations in the corpus

• TASI Lectures on the Emergence of Bulk Physics in AdS/CFT (2017, background): “There are many important references for this material, including [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16].”
• The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole (2019, background): “The physics in the wedge WA can then be reconstructed from field theory degrees of freedom in A [6–9].”
• A general proof of the quantum null energy condition (2017, background): “holographic theory. If the QNEC is violated then as one moves slightly inwards in the holographic zdirection the two bulk entanglement wedges for A and Bwill come into causal contact. Since the JLMS [37] result tells us that boundary modular ow equals bulk modular ow, a similar algebra for modular H”
• Bulk locality from modular flow (2017, methodology): “In theories with a holographic dual, one can think of the modular hamiltonian as an operator in bulk perturbation theory and it is given by [11, 10]:”
• Entropy, extremality, euclidean variations, and the equations of motion (2017, methodology): “Note also that this expression for the modular Hamiltonian is compatible with [24].”
• Entanglement islands in higher dimensions (2019, methodology): “Furthermore, the bulk region between the QES and the boundary, the entanglement wedge, can be reconstructed just using the knowledge of the corresponding boundary subregion [6–11].”
• Quantum extremal islands made easy. Part I. Entanglement on the brane (2020, methodology): “Let us add that from the bulk perspective, entanglement wedge reconstruction [88–94] ensures”
• Low-dimensional de Sitter quantum gravity (2019, background): “[87–97]), it should be fruitful to import these ideas to study the emergence of time in de Sitter.”
• Information flow in black hole evaporation (2019, background): “By entanglement wedge reconstruction [1, 25–30], this implies that after some time, QML plus the bath contain information about the interior of the black hole.”
• Replica wormholes and the black hole interior (2019, background): “not apply [30, 31, 32, 33]. The ER=EPR proposal [33] suggested that a geometric connection might play a role in this identication. 6This was originally conjectured in [34, 35, 6], and established in [36, 37, 38] using the ideas of [8] 7A partial exception is [39], but it does not immediately apply t”
• The Ryu–Takayanagi Formula from Quantum Error Correction (2016, methodology): “20) are precisely the main results of [17]; we now see they are general consequences of subsystem coding with complementary recovery.”