The gravity dual of Rényi entropy

Dong, Xi

doi:10.1038/ncomms12472

The gravity dual of Rényi entropy

Journal Article · Fri Aug 12 00:00:00 EDT 2016 · Nature Communications

DOI:https://doi.org/10.1038/ncomms12472· OSTI ID:1358548

^[1]

Inst. for Advanced Study, Princeton, NJ (United States). School of Natural Sciences; Princeton University

A remarkable yet mysterious property of black holes is that their entropy is proportional to the horizon area. This area law inspired the holographic principle, which was later realized concretely in gauge-gravity duality. In this context, entanglement entropy is given by the area of a minimal surface in a dual spacetime. However, discussions of area laws have been constrained to entanglement entropy, whereas a full understanding of a quantum state requires Re´nyi entropies. Here we show that all Rényi entropies satisfy a similar area law in holographic theories and are given by the areas of dual cosmic branes. This geometric prescription is a one-parameter generalization of the minimal surface prescription for entanglement entropy. Applying this we provide the first holographic calculation of mutual Re´nyi information between two disks of arbitrary dimension. Our results provide a framework for efficiently studying Re´nyi entropies and understanding entanglement structures in strongly coupled systems and quantum gravity.

View Accepted Manuscript (DOE)

Research Organization:: Princeton Univ., NJ (United States)

Sponsoring Organization:: National Science Foundation (NSF); USDOE Office of Science (SC)

Grant/Contract Number:: SC0009988

OSTI ID:: 1358548

Journal Information:: Nature Communications, Journal Name: Nature Communications Vol. 7; ISSN 2041-1723

Publisher:: Nature Publishing GroupCopyright Statement

Country of Publication:: United States

Language:: English

References (88)

Universality in the geometric dependence of Rényi entropy Lewkowycz, Aitor; Perlmutter, Eric Journal of High Energy Physics, Vol. 2015, Issue 1 https://doi.org/10.1007/jhep01(2015)080	journal	January 2015
Rényi entropies for free field theories Klebanov, Igor R.; Pufu, Silviu S.; Sachdev, Subir Journal of High Energy Physics, Vol. 2012, Issue 4 https://doi.org/10.1007/jhep04(2012)074	journal	April 2012
Entanglement Rényi entropies in conformal field theories and holography Fursaev, D. V. Journal of High Energy Physics, Vol. 2012, Issue 5 https://doi.org/10.1007/jhep05(2012)080	journal	May 2012
Topological aspects of generalized gravitational entropy Haehl, Felix M.; Hartman, Thomas; Marolf, Donald Journal of High Energy Physics, Vol. 2015, Issue 5 https://doi.org/10.1007/jhep05(2015)023	journal	May 2015
Holographic entanglement beyond classical gravity Barrella, Taylor; Dong, Xi; Hartnoll, Sean A. Journal of High Energy Physics, Vol. 2013, Issue 9 https://doi.org/10.1007/jhep09(2013)109	journal	September 2013
Geometric and renormalized entropy in conformal field theory Holzhey, Christoph; Larsen, Finn; Wilczek, Frank Nuclear Physics B, Vol. 424, Issue 3 https://doi.org/10.1016/0550-3213(94)90402-2	journal	August 1994
Gravitational field of vacuum domain walls and strings Vilenkin, Alexander Physical Review D, Vol. 23, Issue 4 https://doi.org/10.1103/physrevd.23.852	journal	February 1981
Quantum source of entropy for black holes Bombelli, Luca; Koul, Rabinder K.; Lee, Joohan Physical Review D, Vol. 34, Issue 2 https://doi.org/10.1103/physrevd.34.373	journal	July 1986
Rényi entropy and geometry Lee, Jeongseog; McGough, Lauren; Safdi, Benjamin R. Physical Review D, Vol. 89, Issue 12 https://doi.org/10.1103/physrevd.89.125016	journal	June 2014
Entropy and area Srednicki, Mark Physical Review Letters, Vol. 71, Issue 5 https://doi.org/10.1103/physrevlett.71.666	journal	August 1993
Holographic Derivation of Entanglement Entropy from the anti–de Sitter Space/Conformal Field Theory Correspondence Ryu, Shinsei; Takayanagi, Tadashi Physical Review Letters, Vol. 96, Issue 18 https://doi.org/10.1103/physrevlett.96.181602	journal	May 2006
Rényi entropy and conformal defects Bianchi, Lorenzo; Meineri, Marco; Myers, Robert C. Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/pubdb-2016-05957	text	January 2016
Quantum corrections to holographic entanglement entropy Faulkner, Thomas; Lewkowycz, Aitor; Maldacena, Juan arXiv https://doi.org/10.48550/arxiv.1307.2892	text	January 2013
Renyi entropy, stationarity, and entanglement of the conformal scalar Lee, Jeongseog; Lewkowycz, Aitor; Perlmutter, Eric arXiv https://doi.org/10.48550/arxiv.1407.7816	text	January 2014
The holographic supersymmetric Renyi entropy in five dimensions Alday, Luis F.; Richmond, Paul; Sparks, James arXiv https://doi.org/10.48550/arxiv.1410.0899	text	January 2014
Supersymmetric Renyi Entropy in $CFT_2$ and $AdS_3$ Giveon, Amit; Kutasov, David arXiv https://doi.org/10.48550/arxiv.1510.08872	text	January 2015
Shape Dependence of Holographic Renyi Entropy in Conformal Field Theories Dong, Xi arXiv https://doi.org/10.48550/arxiv.1602.08493	text	January 2016
Cool horizons for entangled black holes Maldacena, J.; Susskind, L. Fortschritte der Physik, Vol. 61, Issue 9 https://doi.org/10.1002/prop.201300020	journal	August 2013
Implications of Conformal Invariance in Field Theories for General Dimensions Osborn, H.; Petkou, A. Annals of Physics, Vol. 231, Issue 2 https://doi.org/10.1006/aphy.1994.1045	journal	May 1994
The four laws of black hole mechanics Bardeen, J. M.; Carter, B.; Hawking, S. W. Communications in Mathematical Physics, Vol. 31, Issue 2 https://doi.org/10.1007/BF01645742	journal	June 1973
Particle creation by black holes Hawking, S. W. Communications In Mathematical Physics, Vol. 43, Issue 3 https://doi.org/10.1007/BF02345020	journal	August 1975
Holographic entanglement entropy for general higher derivative gravity Dong, Xi Journal of High Energy Physics, Vol. 2014, Issue 1 https://doi.org/10.1007/JHEP01(2014)044	journal	January 2014
Quantum extremal surfaces: holographic entanglement entropy beyond the classical regime Engelhardt, Netta; Wall, Aron C. Journal of High Energy Physics, Vol. 2015, Issue 1 https://doi.org/10.1007/JHEP01(2015)073	journal	January 2015
Universality in the geometric dependence of Rényi entropy Lewkowycz, Aitor; Perlmutter, Eric Journal of High Energy Physics, Vol. 2015, Issue 1 https://doi.org/10.1007/JHEP01(2015)080	journal	January 2015
Supersymmetric Renyi entropy in CFT 2 and AdS 3 Giveon, Amit; Kutasov, David Journal of High Energy Physics, Vol. 2016, Issue 1 https://doi.org/10.1007/JHEP01(2016)042	journal	January 2016
The holographic supersymmetric Rényi entropy in five dimensions Alday, Luis F.; Richmond, Paul; Sparks, James Journal of High Energy Physics, Vol. 2015, Issue 2 https://doi.org/10.1007/JHEP02(2015)102	journal	February 2015
Holographic GB gravity in arbitrary dimensions Buchel, Alex; Escobedo, Jorge; Myers, Robert C. Journal of High Energy Physics, Vol. 2010, Issue 3 https://doi.org/10.1007/JHEP03(2010)111	journal	March 2010
Generalized entropy and higher derivative gravity Camps, Joan Journal of High Energy Physics, Vol. 2014, Issue 3 https://doi.org/10.1007/JHEP03(2014)070	journal	March 2014
A universal feature of CFT Rényi entropy Perlmutter, Eric Journal of High Energy Physics, Vol. 2014, Issue 3 https://doi.org/10.1007/JHEP03(2014)117	journal	March 2014
Rényi entropy, stationarity, and entanglement of the conformal scalar Lee, Jeongseog; Lewkowycz, Aitor; Perlmutter, Eric Journal of High Energy Physics, Vol. 2015, Issue 3 https://doi.org/10.1007/JHEP03(2015)075	journal	March 2015
Rényi entropies for free field theories Klebanov, Igor R.; Pufu, Silviu S.; Sachdev, Subir Journal of High Energy Physics, Vol. 2012, Issue 4 https://doi.org/10.1007/JHEP04(2012)074	journal	April 2012
Holographic Rényi entropy for CFT with W symmetry Chen, Bin; Long, Jiang; Zhang, Jia-ju Journal of High Energy Physics, Vol. 2014, Issue 4 https://doi.org/10.1007/JHEP04(2014)041	journal	April 2014
Rényi entropies of free bosons on the torus and holography Datta, Shouvik; David, Justin R. Journal of High Energy Physics, Vol. 2014, Issue 4 https://doi.org/10.1007/JHEP04(2014)081	journal	April 2014
Towards a derivation of holographic entanglement entropy Casini, Horacio; Huerta, Marina; Myers, Robert C. Journal of High Energy Physics, Vol. 2011, Issue 5 https://doi.org/10.1007/JHEP05(2011)036	journal	May 2011
Entanglement Rényi entropies in conformal field theories and holography Fursaev, D. V. Journal of High Energy Physics, Vol. 2012, Issue 5 https://doi.org/10.1007/JHEP05(2012)080	journal	May 2012
Comments on Rényi entropy in AdS3/CFT2 Perlmutter, Eric Journal of High Energy Physics, Vol. 2014, Issue 5 https://doi.org/10.1007/JHEP05(2014)052	journal	May 2014
Topological aspects of generalized gravitational entropy Haehl, Felix M.; Hartman, Thomas; Marolf, Donald Journal of High Energy Physics, Vol. 2015, Issue 5 https://doi.org/10.1007/JHEP05(2015)023	journal	May 2015
Rényi entropies, the analytic bootstrap, and 3D quantum gravity at higher genus Headrick, Matthew; Maloney, Alexander; Perlmutter, Eric Journal of High Energy Physics, Vol. 2015, Issue 7 https://doi.org/10.1007/JHEP07(2015)059	journal	July 2015
Rényi entropy and conformal defects Bianchi, Lorenzo; Meineri, Marco; Myers, Robert C. Journal of High Energy Physics, Vol. 2016, Issue 7 https://doi.org/10.1007/JHEP07(2016)076	journal	July 2016
Holographic Rényi entropies at finite coupling Galante, Damián A.; Myers, Robert C. Journal of High Energy Physics, Vol. 2013, Issue 8 https://doi.org/10.1007/JHEP08(2013)063	journal	August 2013
Generalized gravitational entropy Lewkowycz, Aitor; Maldacena, Juan Journal of High Energy Physics, Vol. 2013, Issue 8 https://doi.org/10.1007/JHEP08(2013)090	journal	August 2013
Holographic entanglement entropy for the most general higher derivative gravity Miao, Rong-Xin; Guo, Wu-zhong Journal of High Energy Physics, Vol. 2015, Issue 8 https://doi.org/10.1007/JHEP08(2015)031	journal	August 2015
Virasoro conformal blocks in closed form Perlmutter, Eric Journal of High Energy Physics, Vol. 2015, Issue 8 https://doi.org/10.1007/JHEP08(2015)088	journal	August 2015
Supersymmetric Rényi entropy Nishioka, Tatsuma; Yaakov, Itamar Journal of High Energy Physics, Vol. 2013, Issue 10 https://doi.org/10.1007/JHEP10(2013)155	journal	October 2013
Twist operators in higher dimensions Hung, Ling-Yan; Myers, Robert C.; Smolkin, Michael Journal of High Energy Physics, Vol. 2014, Issue 10 https://doi.org/10.1007/JHEP10(2014)178	journal	October 2014
Quantum corrections to holographic entanglement entropy Faulkner, Thomas; Lewkowycz, Aitor; Maldacena, Juan Journal of High Energy Physics, Vol. 2013, Issue 11 https://doi.org/10.1007/JHEP11(2013)074	journal	November 2013
On short interval expansion of Rényi entropy Chen, Bin; Zhang, Jia-ju Journal of High Energy Physics, Vol. 2013, Issue 11 https://doi.org/10.1007/JHEP11(2013)164	journal	November 2013
Holographic reconstruction of general bulk surfaces Czech, Bartlomiej; Dong, Xi; Sully, James Journal of High Energy Physics, Vol. 2014, Issue 11 https://doi.org/10.1007/JHEP11(2014)015	journal	November 2014
Holographic duality from random tensor networks Hayden, Patrick; Nezami, Sepehr; Qi, Xiao-Liang Journal of High Energy Physics, Vol. 2016, Issue 11 https://doi.org/10.1007/JHEP11(2016)009	journal	November 2016
Holographic calculations of Rényi entropy Hung, Ling-Yan; Myers, Robert C.; Smolkin, Michael Journal of High Energy Physics, Vol. 2011, Issue 12 https://doi.org/10.1007/JHEP12(2011)047	journal	December 2011
Holographic phases of Rényi entropies Belin, Alexandre; Maloney, Alexander; Matsuura, Shunji Journal of High Energy Physics, Vol. 2013, Issue 12 https://doi.org/10.1007/JHEP12(2013)050	journal	December 2013
Holographic charged Rényi entropies Belin, Alexandre; Hung, Ling-Yan; Maloney, Alexander Journal of High Energy Physics, Vol. 2013, Issue 12 https://doi.org/10.1007/JHEP12(2013)059	journal	December 2013
Particle creation by black holes Hawking, S. W. Communications in Mathematical Physics, Vol. 46, Issue 2 https://doi.org/10.1007/bf01608497	journal	June 1976
Building up spacetime with quantum entanglement Van Raamsdonk, Mark General Relativity and Gravitation, Vol. 42, Issue 10 https://doi.org/10.1007/s10714-010-1034-0	journal	June 2010
Gauge theory correlators from non-critical string theory Gubser, S. S.; Klebanov, I. R.; Polyakov, A. M. Physics Letters B, Vol. 428, Issue 1-2 https://doi.org/10.1016/S0370-2693(98)00377-3	journal	May 1998
Thermodynamics of Chaotic Systems Beck, Christian; Schögl, Friedrich Cambridge University Press https://doi.org/10.1017/CBO9780511524585	journal	January 2009
Measuring entanglement entropy in a quantum many-body system Islam, Rajibul; Ma, Ruichao; Preiss, Philipp M. Nature, Vol. 528, Issue 7580 https://doi.org/10.1038/nature15750	journal	December 2015
The world as a hologram Susskind, Leonard Journal of Mathematical Physics, Vol. 36, Issue 11 https://doi.org/10.1063/1.531249	journal	November 1995
The large N limit of superconformal field theories and supergravity Maldacena, Juan The second meeting on trends in theoretical physics, AIP Conference Proceedings https://doi.org/10.1063/1.59653	conference	January 1999
A covariant holographic entanglement entropy proposal Hubeny, Veronika E.; Rangamani, Mukund; Takayanagi, Tadashi Journal of High Energy Physics, Vol. 2007, Issue 07 https://doi.org/10.1088/1126-6708/2007/07/062	journal	July 2007
Entanglement entropy of two disjoint intervals in conformal field theory Calabrese, Pasquale; Cardy, John; Tonni, Erik Journal of Statistical Mechanics: Theory and Experiment, Vol. 2009, Issue 11 https://doi.org/10.1088/1742-5468/2009/11/P11001	journal	November 2009
Measuring Renyi Entanglement Entropy in Quantum Monte Carlo Simulations Hastings, Matthew B.; González, Iván; Kallin, Ann B. Physical Review Letters, Vol. 104, Issue 15 https://doi.org/10.1103/PhysRevLett.104.157201	journal	April 2010
Shape Dependence of Holographic Rényi Entropy in Conformal Field Theories Dong, Xi Physical Review Letters, Vol. 116, Issue 25 https://doi.org/10.1103/PhysRevLett.116.251602	journal	June 2016
Entropy and area Srednicki, Mark Physical Review Letters, Vol. 71, Issue 5 https://doi.org/10.1103/PhysRevLett.71.666	journal	August 1993
Thermodynamics of Spacetime: The Einstein Equation of State Jacobson, Ted Physical Review Letters, Vol. 75, Issue 7 https://doi.org/10.1103/PhysRevLett.75.1260	journal	August 1995
Holographic Derivation of Entanglement Entropy from the anti–de Sitter Space/Conformal Field Theory Correspondence Ryu, Shinsei; Takayanagi, Tadashi Physical Review Letters, Vol. 96, Issue 18 https://doi.org/10.1103/PhysRevLett.96.181602	journal	May 2006
Colloquium : Area laws for the entanglement entropy Eisert, J.; Cramer, M.; Plenio, M. B. Reviews of Modern Physics, Vol. 82, Issue 1 https://doi.org/10.1103/RevModPhys.82.277	journal	February 2010
Building up Space–Time with Quantum Entanglement Van Raamsdonk, Mark International Journal of Modern Physics D, Vol. 19, Issue 14 https://doi.org/10.1142/s0218271810018529	journal	December 2010
The large $N$ limit of superconformal field theories and supergravity Maldacena, Juan Advances in Theoretical and Mathematical Physics, Vol. 2, Issue 2 https://doi.org/10.4310/ATMP.1998.v2.n2.a1	journal	January 1998
Anti de Sitter space and holography Witten, Edward Advances in Theoretical and Mathematical Physics, Vol. 2, Issue 2 https://doi.org/10.4310/ATMP.1998.v2.n2.a2	journal	January 1998
A Covariant Holographic Entanglement Entropy Proposal Hubeny, Veronika E.; Rangamani, Mukund; Takayanagi, Tadashi arXiv https://doi.org/10.48550/arxiv.0705.0016	text	January 2007
Holographic GB gravity in arbitrary dimensions Buchel, Alex; Escobedo, Jorge; Myers, Robert C. arXiv https://doi.org/10.48550/arxiv.0911.4257	text	January 2009
Towards a derivation of holographic entanglement entropy Casini, Horacio; Huerta, Marina; Myers, Robert C. arXiv https://doi.org/10.48550/arxiv.1102.0440	text	January 2011
Generalized gravitational entropy Lewkowycz, Aitor; Maldacena, Juan arXiv https://doi.org/10.48550/arxiv.1304.4926	text	January 2013
Cool horizons for entangled black holes Maldacena, Juan; Susskind, Leonard arXiv https://doi.org/10.48550/arxiv.1306.0533	text	January 2013
Supersymmetric Renyi Entropy Nishioka, Tatsuma; Yaakov, Itamar arXiv https://doi.org/10.48550/arxiv.1306.2958	text	January 2013
Holographic Entanglement Entropy for General Higher Derivative Gravity Dong, Xi arXiv https://doi.org/10.48550/arxiv.1310.5713	text	January 2013
Holographic Reconstruction of General Bulk Surfaces Czech, Bartlomiej; Dong, Xi; Sully, James arXiv https://doi.org/10.48550/arxiv.1406.4889	text	January 2014
Quantum Extremal Surfaces: Holographic Entanglement Entropy beyond the Classical Regime Engelhardt, Netta; Wall, Aron C. arXiv https://doi.org/10.48550/arxiv.1408.3203	text	January 2014
Holographic Entanglement Entropy for the Most General Higher Derivative Gravity Miao, Rong-Xin; Guo, Wu-zhong arXiv https://doi.org/10.48550/arxiv.1411.5579	text	January 2014
Topological aspects of generalized gravitational entropy Haehl, Felix M.; Hartman, Thomas; Marolf, Donald arXiv https://doi.org/10.48550/arxiv.1412.7561	text	January 2014
Virasoro conformal blocks in closed form Perlmutter, Eric arXiv https://doi.org/10.48550/arxiv.1502.07742	text	January 2015
Holographic duality from random tensor networks Hayden, Patrick; Nezami, Sepehr; Qi, Xiao-Liang arXiv https://doi.org/10.48550/arxiv.1601.01694	text	January 2016
Thermodynamics of Spacetime: The Einstein Equation of State Jacobson, Ted arXiv https://doi.org/10.48550/arxiv.gr-qc/9504004	text	January 1995
The World as a Hologram Susskind, L. arXiv https://doi.org/10.48550/arxiv.hep-th/9409089	text	January 1994
The Large N Limit of Superconformal Field Theories and Supergravity Maldacena, Juan M. arXiv https://doi.org/10.48550/arxiv.hep-th/9711200	text	January 1997
Gauge Theory Correlators from Non-Critical String Theory Gubser, S. S.; Klebanov, I. R.; Polyakov, A. M. arXiv https://doi.org/10.48550/arxiv.hep-th/9802109	text	January 1998
Anti De Sitter Space And Holography Witten, Edward arXiv https://doi.org/10.48550/arxiv.hep-th/9802150	text	January 1998

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Entanglement entropy: Holography and renormalization group Nishioka, Tatsuma Reviews of Modern Physics, Vol. 90, Issue 3 https://doi.org/10.1103/revmodphys.90.035007	journal	September 2018
Holographic subregion complexity for singular surfaces Bakhshaei, Elaheh; Mollabashi, Ali; Shirzad, Ahmad The European Physical Journal C, Vol. 77, Issue 10 https://doi.org/10.1140/epjc/s10052-017-5247-1	journal	October 2017
What’s the point? Hole-ography in Poincaré AdS Espíndola, Ricardo; Güijosa, Alberto; Landetta, Alberto The European Physical Journal C, Vol. 78, Issue 1 https://doi.org/10.1140/epjc/s10052-018-5563-0	journal	January 2018
Exploring the gauge/gravity duality of a generalized von Neumann entropy Cabo Bizet, Nana; Obregón, Octavio The European Physical Journal Plus, Vol. 133, Issue 2 https://doi.org/10.1140/epjp/i2018-11883-5	journal	February 2018
QCD, with strings attached Güijosa, Alberto International Journal of Modern Physics E, Vol. 25, Issue 10 https://doi.org/10.1142/s021830131630006x	journal	October 2016
Bulk entanglement entropy in perturbative excited states Belin, Alexandre; Iqbal, Nabil; Lokhande, Sagar F. SciPost Physics, Vol. 5, Issue 3 https://doi.org/10.21468/scipostphys.5.3.024	journal	January 2018
A Generalized Relative (α, β)-Entropy: Geometric Properties and Applications to Robust Statistical Inference Ghosh, Abhik; Basu, Ayanendranath Entropy, Vol. 20, Issue 5 https://doi.org/10.3390/e20050347	journal	May 2018
Rényi and Tsallis Entropies of the Aharonov–Bohm Ring in Uniform Magnetic Fields Olendski, Oleg Entropy, Vol. 21, Issue 11 https://doi.org/10.3390/e21111060	journal	October 2019
Holographic duality from random tensor networks Hayden, Patrick; Nezami, Sepehr; Qi, Xiao-Liang arXiv https://doi.org/10.48550/arxiv.1601.01694	text	January 2016
Deriving covariant holographic entanglement Dong, Xi; Lewkowycz, Aitor; Rangamani, Mukund arXiv https://doi.org/10.48550/arxiv.1607.07506	text	January 2016
QCD, with Strings Attached Guijosa, Alberto arXiv https://doi.org/10.48550/arxiv.1611.07472	text	January 2016
Gauge protected entanglement between gravity and matter Paunkovic, Nikola; Vojinovic, Marko arXiv https://doi.org/10.48550/arxiv.1702.07744	text	January 2017
Holographic coherent states from random tensor networks Qi, Xiao-Liang; Yang, Zhao; You, Yi-Zhuang arXiv https://doi.org/10.48550/arxiv.1703.06533	text	January 2017
Entanglement, quantum randomness, and complexity beyond scrambling Liu, Zi-Wen; Lloyd, Seth; Zhu, Elton Yechao arXiv https://doi.org/10.48550/arxiv.1703.08104	text	January 2017
Spread of entanglement in a Sachdev-Ye-Kitaev chain Gu, Yingfei; Lucas, Andrew; Qi, Xiao-Liang arXiv https://doi.org/10.48550/arxiv.1708.00871	text	January 2017
What's the Point? Hole-ography in Poincare AdS Espíndola, Ricardo; Guijosa, Alberto; Landetta, Alberto arXiv https://doi.org/10.48550/arxiv.1708.02958	text	January 2017
Machine Learning Spatial Geometry from Entanglement Features You, Yi-Zhuang; Yang, Zhao; Qi, Xiao-Liang arXiv https://doi.org/10.48550/arxiv.1709.01223	text	January 2017
Expanding the Black Hole Interior: Partially Entangled Thermal States in SYK Goel, Akash; Lam, Ho Tat; Turiaci, Gustavo J. arXiv https://doi.org/10.48550/arxiv.1807.03916	text	January 2018
Entanglement negativity and minimal entanglement wedge cross sections in holographic theories Kudler-Flam, Jonah; Ryu, Shinsei arXiv https://doi.org/10.48550/arxiv.1808.00446	text	January 2018
Holographic Renyi Entropy from Quantum Error Correction Akers, Chris; Rath, Pratik arXiv https://doi.org/10.48550/arxiv.1811.05171	text	January 2018
Flat entanglement spectra in fixed-area states of quantum gravity Dong, Xi; Harlow, Daniel; Marolf, Donald arXiv https://doi.org/10.48550/arxiv.1811.05382	text	January 2018
Beyond Toy Models: Distilling Tensor Networks in Full AdS/CFT Bao, Ning; Penington, Geoffrey; Sorce, Jonathan arXiv https://doi.org/10.48550/arxiv.1812.01171	text	January 2018
De Sitter Space and Entanglement Arias, Cesar; Diaz, Felipe; Sundell, Per arXiv https://doi.org/10.48550/arxiv.1901.04554	text	January 2019
Quantum vs. classical information: operator negativity as a probe of scrambling Kudler-Flam, Jonah; Nozaki, Masahiro; Ryu, Shinsei arXiv https://doi.org/10.48550/arxiv.1906.07639	text	January 2019
Renormalized AdS gravity and holographic entanglement entropy of even-dimensional CFTs Anastasiou, Giorgos; Araya, Ignacio J.; Guijosa, Alberto arXiv https://doi.org/10.48550/arxiv.1908.11447	text	January 2019

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