Quantum extremal surfaces: holographic entanglement entropy beyond the classical regime
By Netta Engelhardt, Aron C. Wall. 2014
768 citations recorded by the source corpus.
A bstractWe propose that holographic entanglement entropy can be calculated at arbitrary orders in the bulk Planck constant using the concept of a “quantum extremal surface”: a surface which extremizes the generalized entropy, i.e. the sum of area and bulk entanglement entropy. At leading order in bulk quantum corrections, our proposal agrees with the formula of Faulkner, Lewkowycz, and Maldacena, which was derived only at this order; beyond leading order corrections, the two conjectures diverge. Quantum extremal surfaces lie outside the causal domain of influence of the boundary region as well as its complement, and in some spacetimes there are barriers preventing them from entering certain regions. We comment on the implications for bulk reconstruction.
Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/24515e7e5730398d3b31bd9ad78b25290afeadb5
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Citations in the corpus
- Islands in cosmology (2020, background): “Condition (2) is related to results of Engelhardt and Wall on quantum extremal surface barriers [17] and it was derived for islands in [11, §5] as we will review below.”
- Lessons from the information paradox (2020, background): “To address these paradoxes, we review how the black-hole interior can be con- structed in AdS/CFT.”
- Quantum extremal islands made easy. Part I. Entanglement on the brane (2020, methodology): “This makes contact with the usual notion of generalized entropy as the sum of the geometric gravitational entropy and the entropy of the quantum fields [18, 19].”
- Massive islands (2020, methodology): “One of the key ingredients in both the Page curve calculations of [3, 4] and the construction of entanglement islands in higher dimensions [17] is the use of a fully quantum version [27] of the Ryu-Takayanagi (RT) entropy formula [28].”
- Modular Hamiltonians for deformed half-spaces and the averaged null energy condition (2016, background): “The result (76) arises as a consequence of the formula for quantum corrections to the Ryu-Takaynagi entropy [56,57] (see also [58].”
- The Page curve of Hawking radiation from semiclassical geometry (2019, methodology): “Indeed, interesting recent work [8, 9] addressed the closely related problem of studying the evolution of the von Neumann entropy of an evaporating black hole via the minimal quantum extremal surface (QES) prescription of [7].”
- Proof of the Quantum Null Energy Condition (2015, background): “A generalized entropy can be ascribed not only to horizon slices, but to any surface that splits a Cauchy surface [28–32].”
- TASI Lectures on the Emergence of Bulk Physics in AdS/CFT (2017, background): “There is in fact a proposed generalization to all orders in G [79], which has recently been argued for [80], but there are many new subtleties which arise.”
- Quantum extremal islands made easy. Part II. Black holes on the brane (2020, methodology): “e to compute the Page curve in a controlled manner [13{15]. The new approach builds on insights coming from holographic entanglement entropy [16{19] and its extension to include quantum contributions [20,21]. It is best understood in a setting where a black hole is coupled to an auxiliary, non-gravi”
- Entropy, extremality, euclidean variations, and the equations of motion (2017, background): “This is the quantum extremality condition of [23].”
- Information flow in black hole evaporation (2019, methodology): “n is determined by the Ryu-Takayanagi (stationary area) surface; but at next-to-leading order, corrections arise from the entanglement of bulk elds, specically as computed by the von Neumann entropy [31,32]. The quantum prescription is to instead minimize the generalized entropy, dened by S gen[C] =”
- Islands in Schwarzschild black holes (2020, background): “According to the prescription of the minimal quantum extremal surface [9–11], states in some regions in R, which are called islands I(⊂ R), should be excluded from the states to be traced out.”
- Islands in asymptotically flat 2D gravity (2020, background): “Recent proposed generalizations of this formula define an ‘island rule entropy’ for time-dependent evaporating black holes in AdS - and even for those in flat space - involving a ‘quantum extremal surface’ or QES [8–10].”
- Maximin surfaces, and the strong subadditivity of the covariant holographic entanglement entropy (2012, background): “n, just as in Theorem 6. It therefore seems likely that e.g. the proof of strong subadditivity can also be extended to the semiclassical regime in this way. This topic will be explored in future work [53]. 15An exception might be the monogamy of mutual information (Theorem 19), which does not genera”
- A general proof of the quantum null energy condition (2017, methodology): “ the quantum null energy condition, which was the original goal of this study. The exact surface that we reconstructed should likely be compared to the quantum corrected extremal surface advocated in [51] which was recently proven, in the context of theories with a gravity dual, to compute the entan”