Including contributions from entanglement islands to the reflected entropy

Chandrasekaran, Venkatesa; Miyaji, Masamichi; Rath, Pratik

doi:10.1103/physrevd.102.086009

Title: Including contributions from entanglement islands to the reflected entropy

Journal Article · 07 October 2020 · Physical Review. D.

DOI: https://doi.org/10.1103/physrevd.102.086009 · OSTI ID:1670829

Chandrasekaran, Venkatesa ^[1];

^[1];

^[1]

Univ. of California, Berkeley, CA (United States)

Recent work has demonstrated the need to include contributions from entanglement islands when computing the entanglement entropy in quantum field theory states coupled to regions of semiclassical gravity. We propose a new formula for the reflected entropy that includes additional contributions from such islands. We derive this formula from the gravitational path integral by finding additional saddles that include generalized replica wormholes. We also demonstrate that our covariant formula satisfies all the inequalities required of the reflected entropy. We use this formula in various examples that demonstrate its relevance in illustrating the structure of multipartite entanglement that are invisible to the entropies.

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Research Organization:: University of California, Berkeley, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP); National Science Foundation (NSF)

Grant/Contract Number:: SC0019380; AC02-05CH11231; PHY1820912

OSTI ID:: 1670829

Alternate ID(s):: OSTI ID: 1701729

Journal Information:: Physical Review. D., Vol. 102, Issue 8; ISSN 2470-0010

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (55)

CFT sewing as the dual of AdS cut-and-paste Marolf, Donald Journal of High Energy Physics, Vol. 2020, Issue 2 https://doi.org/10.1007/JHEP02(2020)152	journal	February 2020
Entanglement wedge reconstruction and the information paradox Penington, Geoffrey Journal of High Energy Physics, Vol. 2020, Issue 9 https://doi.org/10.1007/JHEP09(2020)002	journal	September 2020
Multiboundary wormholes and holographic entanglement Balasubramanian, Vijay; Hayden, Patrick; Maloney, Alexander Classical and Quantum Gravity, Vol. 31, Issue 18 https://doi.org/10.1088/0264-9381/31/18/185015	journal	September 2014
Eternal black holes in anti-de Sitter Maldacena, Juan Journal of High Energy Physics, Vol. 2003, Issue 04 https://doi.org/10.1088/1126-6708/2003/04/021	journal	April 2003
Black hole explosions? Hawking, S. W. Nature, Vol. 248, Issue 5443 https://doi.org/10.1038/248030a0	journal	March 1974
An apologia for firewalls Almheiri, Ahmed; Marolf, Donald; Polchinski, Joseph Journal of High Energy Physics, Vol. 2013, Issue 9 https://doi.org/10.1007/JHEP09(2013)018	journal	September 2013
Holographic Entanglement of Purification from Conformal Field Theories Caputa, Pawel; Miyaji, Masamichi; Takayanagi, Tadashi Physical Review Letters, Vol. 122, Issue 11 https://doi.org/10.1103/PhysRevLett.122.111601	journal	March 2019
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
Quantum and classical correlations inside the entanglement wedge Umemoto, Koji Physical Review D, Vol. 100, Issue 12 https://doi.org/10.1103/PhysRevD.100.126021	journal	December 2019
Entanglement of Purification in Many Body Systems and Symmetry Breaking Bhattacharyya, Arpan; Jahn, Alexander; Takayanagi, Tadashi Physical Review Letters, Vol. 122, Issue 20 https://doi.org/10.1103/PhysRevLett.122.201601	journal	May 2019
Simple holographic models of black hole evaporation Akers, Chris; Engelhardt, Netta; Harlow, Daniel Journal of High Energy Physics, Vol. 2020, Issue 8 https://doi.org/10.1007/JHEP08(2020)032	journal	August 2020
The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole Almheiri, Ahmed; Engelhardt, Netta; Marolf, Donald Journal of High Energy Physics, Vol. 2019, Issue 12 https://doi.org/10.1007/JHEP12(2019)063	journal	December 2019
Entanglement of purification in free scalar field theories Bhattacharyya, Arpan; Takayanagi, Tadashi; Umemoto, Koji Journal of High Energy Physics, Vol. 2018, Issue 4 https://doi.org/10.1007/JHEP04(2018)132	journal	April 2018
Maximin surfaces, and the strong subadditivity of the covariant holographic entanglement entropy Wall, Aron C. Classical and Quantum Gravity, Vol. 31, Issue 22 https://doi.org/10.1088/0264-9381/31/22/225007	journal	November 2014
Entanglement of purification through holographic duality Umemoto, Koji; Takayanagi, Tadashi Nature Physics, Vol. 14, Issue 6 https://doi.org/10.1038/s41567-018-0075-2	journal	March 2018
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
Reconstruction of Bulk Operators within the Entanglement Wedge in Gauge-Gravity Duality Dong, Xi; Harlow, Daniel; Wall, Aron C. Physical Review Letters, Vol. 117, Issue 2 https://doi.org/10.1103/PhysRevLett.117.021601	journal	July 2016
Correlation measures and the entanglement wedge cross-section after quantum quenches in two-dimensional conformal field theories Kudler-Flam, Jonah; Kusuki, Yuya; Ryu, Shinsei Journal of High Energy Physics, Vol. 2020, Issue 4 https://doi.org/10.1007/JHEP04(2020)074	journal	April 2020
Spacetime and universal soft modes: Black holes and beyond Nomura, Yasunori Physical Review D, Vol. 101, Issue 6 https://doi.org/10.1103/PhysRevD.101.066024	journal	March 2020
Aspects of holographic entanglement entropy Ryu, Shinsei; Takayanagi, Tadashi Journal of High Energy Physics, Vol. 2006, Issue 08 https://doi.org/10.1088/1126-6708/2006/08/045	journal	August 2006
Entanglement Wedge Cross Section from the Dual Density Matrix Tamaoka, Kotaro Physical Review Letters, Vol. 122, Issue 14 https://doi.org/10.1103/PhysRevLett.122.141601	journal	April 2019
Three qubits can be entangled in two inequivalent ways Dür, W.; Vidal, G.; Cirac, J. I. Physical Review A, Vol. 62, Issue 6 https://doi.org/10.1103/PhysRevA.62.062314	journal	November 2000
Black holes and random matrices Cotler, Jordan S.; Gur-Ari, Guy; Hanada, Masanori Journal of High Energy Physics, Vol. 2017, Issue 5 https://doi.org/10.1007/JHEP05(2017)118	journal	May 2017
Entropy, extremality, euclidean variations, and the equations of motion Dong, Xi; Lewkowycz, Aitor Journal of High Energy Physics, Vol. 2018, Issue 1 https://doi.org/10.1007/JHEP01(2018)081	journal	January 2018
Time evolution of entanglement entropy from black hole interiors Hartman, Thomas; Maldacena, Juan Journal of High Energy Physics, Vol. 2013, Issue 5 https://doi.org/10.1007/JHEP05(2013)014	journal	May 2013
Quantum maximin surfaces Akers, Chris; Engelhardt, Netta; Penington, Geoff Journal of High Energy Physics, Vol. 2020, Issue 8 https://doi.org/10.1007/JHEP08(2020)140	journal	August 2020
The Page curve of Hawking radiation from semiclassical geometry Almheiri, Ahmed; Mahajan, Raghu; Maldacena, Juan Journal of High Energy Physics, Vol. 2020, Issue 3 https://doi.org/10.1007/JHEP03(2020)149	journal	March 2020
Coarse graining holographic black holes Engelhardt, Netta; Wall, Aron C. Journal of High Energy Physics, Vol. 2019, Issue 5 https://doi.org/10.1007/JHEP05(2019)160	journal	May 2019
The gravity dual of a density matrix Czech, Bartłomiej; Karczmarek, Joanna L.; Nogueira, Fernando Classical and Quantum Gravity, Vol. 29, Issue 15 https://doi.org/10.1088/0264-9381/29/15/155009	journal	July 2012
Decoding the Apparent Horizon: Coarse-Grained Holographic Entropy Engelhardt, Netta; Wall, Aron C. Physical Review Letters, Vol. 121, Issue 21 https://doi.org/10.1103/PhysRevLett.121.211301	journal	November 2018
Entanglement negativity and minimal entanglement wedge cross sections in holographic theories Kudler-Flam, Jonah; Ryu, Shinsei Physical Review D, Vol. 99, Issue 10 https://doi.org/10.1103/PhysRevD.99.106014	journal	May 2019
Replica wormholes and the entropy of Hawking radiation Almheiri, Ahmed; Hartman, Thomas; Maldacena, Juan Journal of High Energy Physics, Vol. 2020, Issue 5 https://doi.org/10.1007/JHEP05(2020)013	journal	May 2020
Entanglement wedge cross section from CFT: dynamics of local operator quench Kusuki, Yuya; Tamaoka, Kotaro Journal of High Energy Physics, Vol. 2020, Issue 2 https://doi.org/10.1007/JHEP02(2020)017	journal	February 2020
Interior of a unitarily evaporating black hole Nomura, Yasunori Physical Review D, Vol. 102, Issue 2 https://doi.org/10.1103/PhysRevD.102.026001	journal	July 2020
Entanglement Wedge Reconstruction via Universal Recovery Channels Cotler, Jordan; Hayden, Patrick; Penington, Geoffrey Physical Review X, Vol. 9, Issue 3 https://doi.org/10.1103/PhysRevX.9.031011	journal	July 2019
Black holes: complementarity or firewalls? Almheiri, Ahmed; Marolf, Donald; Polchinski, Joseph Journal of High Energy Physics, Vol. 2013, Issue 2 https://doi.org/10.1007/JHEP02(2013)062	journal	February 2013
From black hole entropy to energy-minimizing states in QFT Bousso, Raphael; Chandrasekaran, Venkatesa; Shahbazi-Moghaddam, Arvin Physical Review D, Vol. 101, Issue 4 https://doi.org/10.1103/PhysRevD.101.046001	journal	February 2020
Multipartite reflected entropy Bao, Ning; Cheng, Newton Journal of High Energy Physics, Vol. 2019, Issue 10 https://doi.org/10.1007/JHEP10(2019)102	journal	October 2019
Quantum focusing conjecture Bousso, Raphael; Fisher, Zachary; Leichenauer, Stefan Physical Review D, Vol. 93, Issue 6 https://doi.org/10.1103/PhysRevD.93.064044	journal	March 2016
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
Conditional and multipartite entanglements of purification and holography Bao, Ning; Halpern, Illan F. Physical Review D, Vol. 99, Issue 4 https://doi.org/10.1103/PhysRevD.99.046010	journal	February 2019
Entanglement of purification: from spin chains to holography Nguyen, Phuc; Devakul, Trithep; Halbasch, Matthew G. Journal of High Energy Physics, Vol. 2018, Issue 1 https://doi.org/10.1007/JHEP01(2018)098	journal	January 2018
Entanglement wedge cross sections require tripartite entanglement Akers, Chris; Rath, Pratik Journal of High Energy Physics, Vol. 2020, Issue 4 https://doi.org/10.1007/JHEP04(2020)208	journal	April 2020
Four qubits can be entangled in nine different ways Verstraete, F.; Dehaene, J.; De Moor, B. Physical Review A, Vol. 65, Issue 5 https://doi.org/10.1103/PhysRevA.65.052112	journal	April 2002
The information paradox: a pedagogical introduction Mathur, Samir D. Classical and Quantum Gravity, Vol. 26, Issue 22 https://doi.org/10.1088/0264-9381/26/22/224001	journal	October 2009
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
Erratum to: Black holes and random matrices Cotler, Jordan S.; Gur-Ari, Guy; Hanada, Masanori Journal of High Energy Physics, Vol. 2018, Issue 9 https://doi.org/10.1007/JHEP09(2018)002	journal	September 2018
Correlation measures and distillable entanglement in AdS / CFT Levin, Joshua; DeWolfe, Oliver; Smith, Graeme Physical Review D, Vol. 101, Issue 4 https://doi.org/10.1103/PhysRevD.101.046015	journal	February 2020
Comments on entanglement negativity in holographic field theories Rangamani, Mukund; Rota, Massimiliano Journal of High Energy Physics, Vol. 2014, Issue 10 https://doi.org/10.1007/JHEP10(2014)060	journal	October 2014
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 quantum entanglement negativity Chaturvedi, Pankaj; Malvimat, Vinay; Sengupta, Gautam Journal of High Energy Physics, Vol. 2018, Issue 5 https://doi.org/10.1007/JHEP05(2018)172	journal	May 2018
Derivation of Holographic Negativity in AdS 3 / CFT 2 Kusuki, Yuya; Kudler-Flam, Jonah; Ryu, Shinsei Physical Review Letters, Vol. 123, Issue 13 https://doi.org/10.1103/PhysRevLett.123.131603	journal	September 2019
Hot multiboundary wormholes from bipartite entanglement Marolf, Donald; Maxfield, Henry; Peach, Alex Classical and Quantum Gravity, Vol. 32, Issue 21 https://doi.org/10.1088/0264-9381/32/21/215006	journal	October 2015
Entanglement structures in qubit systems Rangamani, Mukund; Rota, Massimiliano Journal of Physics A: Mathematical and Theoretical, Vol. 48, Issue 38 https://doi.org/10.1088/1751-8113/48/38/385301	journal	August 2015
The Python’s Lunch: geometric obstructions to decoding Hawking radiation Brown, Adam R.; Gharibyan, Hrant; Penington, Geoff Journal of High Energy Physics, Vol. 2020, Issue 8 https://doi.org/10.1007/JHEP08(2020)121	journal	August 2020

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