Built on

D. Marolf, A. C. Wall, and Z. Wang, Restricted Maximin surfaces and HRT in generic black hole spacetimes
Original
1901
Earlier work this paper cites.
G. Penington, Entanglement Wedge Reconstruction and the Information Paradox
Original
1905
Earlier work this paper cites.
A. Almheiri, N. Engelhardt, D. Marolf, and H. Maxfield, The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole
Original
1905
Earlier work this paper cites.
S. Balakrishnan, V. Chandrasekaran, T. Faulkner, A. Levine, and A. Shahbazi-Moghaddam, Entropy Variations and Light Ray Operators from Replica Defects
Original
1906
Earlier work this paper cites.
A. Almheiri, R. Mahajan, J. Maldacena, and Y. Zhao, The Page curve of Hawking radiation from semiclassical geometry
Original
1908
Earlier work this paper cites.
X. Dong and D. Marolf, One-loop universality of holographic codes
Original
1910
Earlier work this paper cites.
A. Almheiri, R. Mahajan, and J. Maldacena, Islands outside the horizon
Original
1910
Earlier work this paper cites.
C. Akers, N. Engelhardt, and D. Harlow, Simple holographic models of black hole evaporation
Original
1910
Earlier work this paper cites.
G. Penington, S. H. Shenker, D. Stanford, and Z. Yang, Replica wormholes and the black hole interior
Original
1911
Earlier work this paper cites.
A. Almheiri, T. Hartman, J. Maldacena, E. Shaghoulian, and A. Tajdini, Replica Wormholes and the Entropy of Hawking Radiation
Original
1911
Earlier work this paper cites.
A. Almheiri, R. Mahajan, and J. E. Santos, Entanglement islands in higher dimensions
Original
1911
Earlier work this paper cites.
H. Epstein, V. Glaser, and A. Jaffe, Nonpositivity of the energy density in quantized field theories
1965
Earlier work this paper cites.
J. D. Bekenstein, Black holes and the second law
1972
Earlier work this paper cites.
J. D. Bekenstein, Black holes and entropy
1973
Earlier work this paper cites.
S. W. Hawking, Particle creation by black holes
1975
Earlier work this paper cites.
P. C. W. Davies and S. A. Fulling, Radiation from a moving mirror in two-dimensional space-time conformal anomaly
1976
Earlier work this paper cites.
P. C. W. Davies, S. A. Fulling, and W. G. Unruh, Energy Momentum Tensor Near an Evaporating Black Hole
1976
Earlier work this paper cites.
P. C. W. Davies and S. A. Fulling, Radiation from Moving Mirrors and from Black Holes
1977
Earlier work this paper cites.
The University of Chicago Press, Chicago, 1984
R. M. Wald, General Relativity · 1984
Earlier work this paper cites.

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V. Iyer and R. M. Wald, Some properties of Noether charge and a proposal for dynamical black hole entropy
1994
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Original

Then

N. Engelhardt and A. C. Wall, Quantum Extremal Surfaces: Holographic Entanglement Entropy beyond the Classical Regime
Original
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Later among the works it cites.
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2015
Later among the works it cites.
S. Fischetti, D. Marolf, and A. C. Wall, A paucity of bulk entangling surfaces: AdS wormholes with de Sitter interiors
Original
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2019

Quantum Maximin Surfaces

Akers, Chris, Engelhardt, Netta, Penington, Geoff et al.

Understand

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.

Built on

D. Marolf, A. C. Wall, and Z. Wang, Restricted Maximin surfaces and HRT in generic black hole spacetimes
Original
1901
Earlier work this paper cites.
G. Penington, Entanglement Wedge Reconstruction and the Information Paradox
Original
1905
Earlier work this paper cites.
A. Almheiri, N. Engelhardt, D. Marolf, and H. Maxfield, The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole
Original
1905
Earlier work this paper cites.
S. Balakrishnan, V. Chandrasekaran, T. Faulkner, A. Levine, and A. Shahbazi-Moghaddam, Entropy Variations and Light Ray Operators from Replica Defects
Original
1906
Earlier work this paper cites.
A. Almheiri, R. Mahajan, J. Maldacena, and Y. Zhao, The Page curve of Hawking radiation from semiclassical geometry
Original
1908
Earlier work this paper cites.
X. Dong and D. Marolf, One-loop universality of holographic codes
Original
1910
Earlier work this paper cites.
A. Almheiri, R. Mahajan, and J. Maldacena, Islands outside the horizon
Original
1910
Earlier work this paper cites.
C. Akers, N. Engelhardt, and D. Harlow, Simple holographic models of black hole evaporation
Original
1910
Earlier work this paper cites.
G. Penington, S. H. Shenker, D. Stanford, and Z. Yang, Replica wormholes and the black hole interior
Original
1911
Earlier work this paper cites.
A. Almheiri, T. Hartman, J. Maldacena, E. Shaghoulian, and A. Tajdini, Replica Wormholes and the Entropy of Hawking Radiation
Original
1911
Earlier work this paper cites.
A. Almheiri, R. Mahajan, and J. E. Santos, Entanglement islands in higher dimensions
Original
1911
Earlier work this paper cites.
H. Epstein, V. Glaser, and A. Jaffe, Nonpositivity of the energy density in quantized field theories
1965
Earlier work this paper cites.
J. D. Bekenstein, Black holes and the second law
1972
Earlier work this paper cites.
J. D. Bekenstein, Black holes and entropy
1973
Earlier work this paper cites.
S. W. Hawking, Particle creation by black holes
1975
Earlier work this paper cites.
P. C. W. Davies and S. A. Fulling, Radiation from a moving mirror in two-dimensional space-time conformal anomaly
1976
Earlier work this paper cites.
P. C. W. Davies, S. A. Fulling, and W. G. Unruh, Energy Momentum Tensor Near an Evaporating Black Hole
1976
Earlier work this paper cites.
P. C. W. Davies and S. A. Fulling, Radiation from Moving Mirrors and from Black Holes
1977
Earlier work this paper cites.
The University of Chicago Press, Chicago, 1984
R. M. Wald, General Relativity · 1984
Earlier work this paper cites.

Similar

V. Iyer and R. M. Wald, Some properties of Noether charge and a proposal for dynamical black hole entropy
1994
Cited alongside, same era.
D. V. Fursaev and S. N. Solodukhin, On one loop renormalization of black hole entropy
1996
Cited alongside, same era.
H. B. G. Casimir, On the Attraction Between Two Perfectly Conducting Plates
1997
Cited alongside, same era.
G. J. Galloway, Maximum principles for null hypersurfaces and null splitting theorems
2000
Cited alongside, same era.
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT
2006
Cited alongside, same era.
V. E. Hubeny, M. Rangamani, and T. Takayanagi, A Covariant holographic entanglement entropy proposal
Original

Then

N. Engelhardt and A. C. Wall, Quantum Extremal Surfaces: Holographic Entanglement Entropy beyond the Classical Regime
Original
2015
Later among the works it cites.
R.-X. Miao and W.-z. Guo, Holographic entanglement entropy for the most general higher derivative gravity
2015
Later among the works it cites.
S. Fischetti, D. Marolf, and A. C. Wall, A paucity of bulk entangling surfaces: AdS wormholes with de Sitter interiors
Original
2015
Later among the works it cites.
R. Bousso and N. Engelhardt, Proof of a New Area Law in General Relativity
Original
2015
Later among the works it cites.
N. Bao, S. Nezami, H. Ooguri, B. Stoica, J. Sully, and M. Walter, The Holographic Entropy Cone
Original

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2007

Cited alongside, same era.

M. Headrick and T. Takayanagi, A Holographic proof of the strong subadditivity of entanglement entropy

Original

2007

Cited alongside, same era.

A. C. Wall, Ten Proofs of the Generalized Second Law

Original

2009

Cited alongside, same era.

C.I.M.E. Summer Schools. Springer Berlin Heidelberg, 2011

E. Bombieri, Geometric Measure Theory and Minimal Surfaces: Lectures given at a Summer School of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Varenna (Como), Italy, August 24 - September 2, 1972 · 2011

Cited alongside, same era.

B. Czech, J. L. Karczmarek, F. Nogueira, and M. Van Raamsdonk, The Gravity Dual of a Density Matrix

Original

2012

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P. Hayden, M. Headrick, and A. Maloney, Holographic mutual information is monogamous

2013

Cited alongside, same era.

A. C. Wall, The Generalized Second Law implies a Quantum Singularity Theorem

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2013

Cited alongside, same era.