Towards a bit threads derivation of holographic entanglement of purification

Bao, Ning; Chatwin-Davies, Aidan; Pollack, Jason; Remmen, Grant N.

doi:10.1007/JHEP07(2019)152

Title: Towards a bit threads derivation of holographic entanglement of purification

Journal Article · 25 July 2019 · Journal of High Energy Physics (Online)

DOI: https://doi.org/10.1007/JHEP07(2019)152 · OSTI ID:1566868

Bao, Ning ^[1]; Chatwin-Davies, Aidan ^[2]; Pollack, Jason ^[3]; Remmen, Grant N. ^[4]

Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Brookhaven National Lab. (BNL), Upton, NY (United States)
KU Leuven, Leuven (Belgium)
Univ. of British Columbia, Vancouver, BC (Canada)
Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

We apply the bit thread formulation of holographic entanglement entropy to reduced states describing only the geometry contained within an entanglement wedge. We argue that a certain optimized bit thread configuration, which we construct, gives a purification of the reduced state to a full holographic state obeying a precise set of conditional mutual information relations. When this purification exists, we establish, under certain assumptions, the conjectured E_P = E_W relation equating the entanglement of purification with the area of the minimal cross section partitioning the bulk entanglement wedge. Along the way, we comment on minimal purifications of holographic states, geometric purifications, and black hole geometries.

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Research Organization:: Brookhaven National Laboratory (BNL), Upton, NY (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (SC-21)

Grant/Contract Number:: SC0012704

OSTI ID:: 1566868

Report Number(s):: BNL-212127-2019-JAAM; TRN: US2001005

Journal Information:: Journal of High Energy Physics (Online), Vol. 2019, Issue 7; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

References (47)

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
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
Operator content of two-dimensional conformally invariant theories Cardy, John L. Nuclear Physics B, Vol. 270 https://doi.org/10.1016/0550-3213(86)90552-3	journal	January 1986
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
Connectedness of the boundary in the $\mathrm{AdS}$/$\mathrm{CFT}$ correspondence Witten, Edward; Yau, S. -T. Advances in Theoretical and Mathematical Physics, Vol. 3, Issue 6 https://doi.org/10.4310/ATMP.1999.v3.n6.a1	journal	January 1999
Semiclassical Wheeler wormhole production Garfinkle, David; Strominger, Andrew Physics Letters B, Vol. 256, Issue 2 https://doi.org/10.1016/0370-2693(91)90665-D	journal	March 1991
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
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
The Large-N Limit of Superconformal Field Theories and Supergravity Maldacena, Juan International Journal of Theoretical Physics, Vol. 38, Issue 4, p. 1113-1133 https://doi.org/10.1023/A:1026654312961	journal	January 1999
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
The Ryu–Takayanagi Formula from Quantum Error Correction Harlow, Daniel Communications in Mathematical Physics, Vol. 354, Issue 3 https://doi.org/10.1007/s00220-017-2904-z	journal	May 2017
A continuity property of the entropy density for spin lattice systems Fannes, M. Communications in Mathematical Physics, Vol. 31, Issue 4 https://doi.org/10.1007/BF01646490	journal	December 1973
Splitting spacetime and cloning qubits: linking no-go theorems across the ER=EPR duality: Splitting spacetime and cloning qubits Bao, Ning; Pollack, Jason; Remmen, Grant N. Fortschritte der Physik, Vol. 63, Issue 11-12 https://doi.org/10.1002/prop.201500053	journal	November 2015
Entanglement of purification and multiboundary wormhole geometries Bao, Ning; Chatwin-Davies, Aidan; Remmen, Grant N. Journal of High Energy Physics, Vol. 2019, Issue 2 https://doi.org/10.1007/JHEP02(2019)110	journal	February 2019
Holographic inequalities and entanglement of purification Bao, Ning; Halpern, Illan F. Journal of High Energy Physics, Vol. 2018, Issue 3 https://doi.org/10.1007/JHEP03(2018)006	journal	March 2018
Bit Threads and Holographic Entanglement Freedman, Michael; Headrick, Matthew Communications in Mathematical Physics, Vol. 352, Issue 1 https://doi.org/10.1007/s00220-016-2796-3	journal	November 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
Entanglement of purification for multipartite states and its holographic dual Umemoto, Koji; Zhou, Yang Journal of High Energy Physics, Vol. 2018, Issue 10 https://doi.org/10.1007/JHEP10(2018)152	journal	October 2018
The holographic principle Bousso, Raphael Reviews of Modern Physics, Vol. 74, Issue 3 https://doi.org/10.1103/RevModPhys.74.825	journal	August 2002
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
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
Geometric aspects of holographic bit threads Agón, Cesar A.; de Boer, Jan; Pedraza, Juan F. Journal of High Energy Physics, Vol. 2019, Issue 5 https://doi.org/10.1007/JHEP05(2019)075	journal	May 2019
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
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
Large N field theories, string theory and gravity Aharony, Ofer; Gubser, Steven S.; Maldacena, Juan Physics Reports, Vol. 323, Issue 3-4 https://doi.org/10.1016/S0370-1573(99)00083-6	journal	January 2000
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
Chaos and quantum thermalization Srednicki, Mark Physical Review E, Vol. 50, Issue 2 https://doi.org/10.1103/PhysRevE.50.888	journal	August 1994
Maximal flow through a domain Strang, Gilbert Mathematical Programming, Vol. 26, Issue 2 https://doi.org/10.1007/BF02592050	journal	June 1983
Real Flat Chains, Cochains and Variational Problems Federer, Herbert Indiana University Mathematics Journal, Vol. 24, Issue 4 https://doi.org/10.1512/iumj.1975.24.24031	journal	January 1974
Calibrated geometries Harvey, Reese; Lawson, H. Blaine Acta Mathematica, Vol. 148, Issue 0 https://doi.org/10.1007/BF02392726	journal	January 1982
Linearity of holographic entanglement entropy Almheiri, Ahmed; Dong, Xi; Swingle, Brian Journal of High Energy Physics, Vol. 2017, Issue 2 https://doi.org/10.1007/JHEP02(2017)074	journal	February 2017
Central charges in the canonical realization of asymptotic symmetries: An example from three dimensional gravity Brown, J. D.; Henneaux, Marc Communications in Mathematical Physics, Vol. 104, Issue 2 https://doi.org/10.1007/BF01211590	journal	June 1986
The entanglement of purification Terhal, Barbara M.; Horodecki, Michał; Leung, Debbie W. Journal of Mathematical Physics, Vol. 43, Issue 9 https://doi.org/10.1063/1.1498001	journal	September 2002
Calibrated entanglement entropy Bakhmatov, I.; Deger, N. S.; Gutowski, J. Journal of High Energy Physics, Vol. 2017, Issue 7 https://doi.org/10.1007/JHEP07(2017)117	journal	July 2017
Surface/state correspondence as a generalized holography Miyaji, Masamichi; Takayanagi, Tadashi Progress of Theoretical and Experimental Physics, Vol. 2015, Issue 7 https://doi.org/10.1093/ptep/ptv089	journal	July 2015
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
The Ryu-Takayanagi Formula from Quantum Error Correction Harlow, Daniel arXiv https://doi.org/10.48550/arxiv.1607.03901	text	January 2016
Entanglement of purification: from spin chains to holography Nguyen, Phuc; Devakul, Trithep; Halbasch, Matthew G. arXiv https://doi.org/10.48550/arxiv.1709.07424	text	January 2017
Geometric Aspects of Holographic Bit Threads Agón, Cesar A.; de Boer, Jan; Pedraza, Juan F. arXiv https://doi.org/10.48550/arxiv.1811.08879	text	January 2018
Chaos and Quantum Thermalization Srednicki, Mark arXiv https://doi.org/10.48550/arxiv.cond-mat/9403051	text	January 1994
The holographic principle Bousso, Raphael arXiv https://doi.org/10.48550/arxiv.hep-th/0203101	text	January 2002
Aspects of Holographic Entanglement Entropy Ryu, Shinsei; Takayanagi, Tadashi arXiv https://doi.org/10.48550/arxiv.hep-th/0605073	text	January 2006
The World as a Hologram Susskind, L. arXiv https://doi.org/10.48550/arxiv.hep-th/9409089	text	January 1994
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
Large N Field Theories, String Theory and Gravity Aharony, O.; Gubser, S. S.; Maldacena, J. arXiv https://doi.org/10.48550/arxiv.hep-th/9905111	text	January 1999

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