scholarly journals Quantum maximin surfaces

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
Chris Akers ◽  
Netta Engelhardt ◽  
Geoff Penington ◽  
Mykhaylo Usatyuk
Keyword(s):  
Black Hole ◽  
Von Neumann Entropy ◽  
Quantum Fields ◽  
Extremal Surface ◽  
Von Neumann ◽  
Black Hole Evaporation ◽  
Generalized Entropy ◽  
General Proof ◽  
Strong Subadditivity ◽  
New Models

Abstract We formulate a quantum generalization of maximin surfaces and show that a quantum maximin surface is identical to the minimal quantum extremal surface, introduced in the EW prescription. We discuss various subtleties and complications associated to a maximinimization of the bulk von Neumann entropy due to corners and unboundedness and present arguments that nonetheless a maximinimization of the UV-finite generalized entropy should be well-defined. We give the first general proof that the EW prescription satisfies entanglement wedge nesting and the strong subadditivity inequality. In addition, we apply the quantum maximin technology to prove that recently proposed generalizations of the EW prescription to nonholographic subsystems (including the so-called “quantum extremal islands”) also satisfy entanglement wedge nesting and strong subadditivity. Our results hold in the regime where backreaction of bulk quantum fields can be treated perturbatively in GNħ, but we emphasize that they are valid even when gradients of the bulk entropy are of the same order as variations in the area, a regime recently investigated in new models of black hole evaporation in AdS/CFT.

THE UNREASONABLE EFFECTIVENESS OF EXPONENTIALLY SUPPRESSED CORRECTIONS IN PRESERVING INFORMATION

2013 ◽  
Vol 22 (12) ◽  
pp. 1342030 ◽  
Author(s):  
KYRIAKOS PAPADODIMAS ◽  
SUVRAT RAJU
Keyword(s):  
Hilbert Space ◽  
Black Hole ◽  
Quantum Mechanics ◽  
Nonperturbative Effects ◽  
Von Neumann Entropy ◽  
Von Neumann ◽  
Information Theoretic ◽  
Black Hole Evaporation ◽  
Strong Subadditivity ◽  
Unreasonable Effectiveness

We point out that nonperturbative effects in quantum gravity are sufficient to reconcile the process of black hole evaporation with quantum mechanics. In ordinary processes, these corrections are unimportant because they are suppressed by e-S. However, they gain relevance in information-theoretic considerations because their small size is offset by the corresponding largeness of the Hilbert space. In particular, we show how such corrections can cause the von Neumann entropy of the emitted Hawking quanta to decrease after the Page time, without modifying the thermal nature of each emitted quantum. Second, we show that exponentially suppressed commutators between operators inside and outside the black hole are sufficient to resolve paradoxes associated with the strong subadditivity of entropy without any dramatic modifications of the geometry near the horizon.

scholarly journals Semi-classical thermodynamics of quantum extremal surfaces in Jackiw-Teitelboim gravity

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Juan F. Pedraza ◽  
Andrew Svesko ◽  
Watse Sybesma ◽  
Manus R. Visser
Keyword(s):  
Black Hole ◽  
Central Charge ◽  
Microcanonical Ensemble ◽  
Von Neumann Entropy ◽  
De Sitter ◽  
Von Neumann ◽  
Generalized Entropy ◽  
Conformal Field ◽  
Matter System ◽  
Classical Thermodynamics

Abstract Quantum extremal surfaces (QES), codimension-2 spacelike regions which extremize the generalized entropy of a gravity-matter system, play a key role in the study of the black hole information problem. The thermodynamics of QESs, however, has been largely unexplored, as a proper interpretation requires a detailed understanding of backreaction due to quantum fields. We investigate this problem in semi-classical Jackiw-Teitelboim (JT) gravity, where the spacetime is the eternal two-dimensional Anti-de Sitter (AdS2) black hole, Hawking radiation is described by a conformal field theory with central charge c, and backreaction effects may be analyzed exactly. We show the Wald entropy of the semi-classical JT theory entirely encapsulates the generalized entropy — including time-dependent von Neumann entropy contributions — whose extremization leads to a QES lying just outside of the black hole horizon. Consequently, the QES defines a Rindler wedge nested inside the enveloping black hole. We use covariant phase space techniques on a time-reflection symmetric slice to derive a Smarr relation and first law of nested Rindler wedge thermodynamics, regularized using local counterterms, and intrinsically including semi-classical effects. Moreover, in the microcanonical ensemble the semi-classical first law implies the generalized entropy of the QES is stationary at fixed energy. Thus, the thermodynamics of the nested Rindler wedge is equivalent to the thermodynamics of the QES in the microcanonical ensemble.

scholarly journals Islands in the stream of Hawking radiation

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Timothy J. Hollowood ◽  
S. Prem Kumar ◽  
Andrea Legramandi ◽  
Neil Talwar
Keyword(s):  
Black Hole ◽  
Quantum Information ◽  
Hawking Radiation ◽  
Adiabatic Limit ◽  
Black Hole Evaporation ◽  
Generalized Entropy ◽  
Strong Subadditivity

Abstract We consider the island formula for the entropy of subsets of the Hawking radiation in the adiabatic limit where the black hole evaporation is very slow. We find a simple concrete ‘on-shell’ formula for the generalized entropy which involves the image of the island out in the stream of radiation, the ‘island in the stream’. The resulting recipe for the entropy allows us to calculate the quantum information properties of the radiation and verify various constraints including the Araki-Lieb inequality and strong subadditivity.

scholarly journals Islands in linear dilaton black holes

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Georgios K. Karananas ◽  
Alex Kehagias ◽  
John Taskas
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Entanglement Entropy ◽  
Von Neumann Entropy ◽  
Two Dimensional ◽  
Extremal Case ◽  
Von Neumann ◽  
Dimensional Black Hole ◽  
Linear Dilaton ◽  
Linear Dilaton Black Hole

Abstract We derive a novel four-dimensional black hole with planar horizon that asymptotes to the linear dilaton background. The usual growth of its entanglement entropy before Page’s time is established. After that, emergent islands modify to a large extent the entropy, which becomes finite and is saturated by its Bekenstein-Hawking value in accordance with the finiteness of the von Neumann entropy of eternal black holes. We demonstrate that viewed from the string frame, our solution is the two-dimensional Witten black hole with two additional free bosons. We generalize our findings by considering a general class of linear dilaton black hole solutions at a generic point along the σ-model renormalization group (RG) equations. For those, we observe that the entanglement entropy is “running” i.e. it is changing along the RG flow with respect to the two-dimensional worldsheet length scale. At any fixed moment before Page’s time the aforementioned entropy increases towards the infrared (IR) domain, whereas the presence of islands leads the running entropy to decrease towards the IR at later times. Finally, we present a four-dimensional charged black hole that asymptotes to the linear dilaton background as well. We compute the associated entanglement entropy for the extremal case and we find that an island is needed in order for it to follow the Page curve.

scholarly journals Does spacetime inherently has von Neumann entropy?

2020 ◽  
Author(s):  
William Icefield
Keyword(s):  
Black Hole ◽  
Quantum Theory ◽  
Black Hole Entropy ◽  
Black Hole Thermodynamics ◽  
Von Neumann Entropy ◽  
Considerable Difficulty ◽  
Von Neumann ◽  
Thermodynamic Entropy

There has been considerable difficulty in equating thermodynamic entropy, suggested in classical and black hole thermodynamics, with von Neumann entropy. Successful derivations of black hole entropy from purely classical origins and recent doubts as to whether we can really equate von Neumann entropy with thermodynamic entropy open up the possibility that spacetime inherently encodes entropy. In this understanding, any quantum theory defined on some spacetime or worldsheet inherently calls for another quantum theory that explains entropy encoded by spacetime.

A simple proof of the strong subadditivity inequality

2005 ◽  
Vol 5 (6) ◽  
pp. 507-513
Author(s):  
M.A. Nielsen ◽  
D. Petz
Keyword(s):  
Quantum Mechanics ◽  
Quantum Information ◽  
Linear Algebra ◽  
Simple Proof ◽  
Von Neumann Entropy ◽  
Von Neumann ◽  
Strong Subadditivity ◽  
Math Phys

Arguably the deepest fact known about the von~Neumann entropy, the strong subadditivity inequality is a potent hammer in the quantum information theorist's toolkit. This short tutorial describes a simple proof of strong subadditivity due to Petz [Rep. on Math. Phys. \textbf{23} (1), 57--65 (1986)]. It assumes only knowledge of elementary linear algebra and quantum mechanics.

scholarly journals Linear growth of the entanglement entropy for quadratic Hamiltonians and arbitrary initial states

2022 ◽  
Vol 12 (1) ◽  
Author(s):  
Giacomo De Palma ◽  
Lucas Hackl
Keyword(s):  
Entanglement Entropy ◽  
Quantum Systems ◽  
Von Neumann Entropy ◽  
Classical Dynamics ◽  
Initial State ◽  
Von Neumann ◽  
Strong Subadditivity ◽  
Periodically Driven ◽  
Initial States ◽  
The Right

We prove that the entanglement entropy of any pure initial state of a bipartite bosonic quantum system grows linearly in time with respect to the dynamics induced by any unstable quadratic Hamiltonian. The growth rate does not depend on the initial state and is equal to the sum of certain Lyapunov exponents of the corresponding classical dynamics. This paper generalizes the findings of [Bianchi et al., JHEP 2018, 25 (2018)], which proves the same result in the special case of Gaussian initial states. Our proof is based on a recent generalization of the strong subadditivity of the von Neumann entropy for bosonic quantum systems [De Palma et al., arXiv:2105.05627]. This technique allows us to extend our result to generic mixed initial states, with the squashed entanglement providing the right generalization of the entanglement entropy. We discuss several applications of our results to physical systems with (weakly) interacting Hamiltonians and periodically driven quantum systems, including certain quantum field theory models.

scholarly journals The Holographic Nature of Null Infinity

2021 ◽  
Vol 10 (2) ◽  
Author(s):  
Alok Laddha ◽  
Siddharth Prabhu ◽  
Suvrat Raju ◽  
Pushkal Shrivastava
Keyword(s):  
Flat Space ◽  
The State ◽  
Von Neumann Entropy ◽  
Null Infinity ◽  
Von Neumann ◽  
Black Hole Evaporation ◽  
Asymptotically Flat ◽  
Fine Grained ◽  
The Past ◽  
Future Null Infinity

We argue that, in a theory of quantum gravity in a four dimensional asymptotically flat spacetime, all information about massless excitations can be obtained from an infinitesimal neighbourhood of the past boundary of future null infinity and does not require observations over all of future null infinity. Moreover, all information about the state that can be obtained through observations near a cut of future null infinity can also be obtained from observations near any earlier cut although the converse is not true. We provide independent arguments for these two assertions. Similar statements hold for past null infinity. These statements have immediate implications for the information paradox since they suggest that the fine-grained von Neumann entropy of the state defined on a segment (-infty,u) of future null infinity is independent of u. This is very different from the oft-discussed Page curve that this entropy is sometimes expected to obey. We contrast our results with recent discussions of the Page curve in the context of black hole evaporation, and also discuss the relation of our results to other proposals for holography in flat space.

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