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The Holographic Entropy Cone

Bao, Ning and Nezami, Sepehr and Ooguri, Hirosi and Stoica, Bogdan and Sully, James and Walter, Michael (2015) The Holographic Entropy Cone. Journal of High Energy Physics, 2015 (9). Art. No. 130. ISSN 1126-6708. doi:10.1007/JHEP09(2015)130.

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We initiate a systematic enumeration and classification of entropy inequalities satisfied by the Ryu-Takayanagi formula for conformal field theory states with smooth holographic dual geometries. For 2, 3, and 4 regions, we prove that the strong subadditivity and the monogamy of mutual information give the complete set of inequalities. This is in contrast to the situation for generic quantum systems, where a complete set of entropy inequalities is not known for 4 or more regions. We also find an infinite new family of inequalities applicable to 5 or more regions. The set of all holographic entropy inequalities bounds the phase space of Ryu-Takayanagi entropies, defining the holographic entropy cone. We characterize this entropy cone by reducing geometries to minimal graph models that encode the possible cutting and gluing relations of minimal surfaces. We find that, for a fixed number of regions, there are only finitely many independent entropy inequalities. To establish new holographic entropy inequalities, we introduce a combinatorial proof technique that may also be of independent interest in Riemannian geometry and graph theory.

Item Type:Article
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URLURL TypeDescription Paper DOIArticle
Bao, Ning0000-0002-3296-1039
Ooguri, Hirosi0000-0001-6021-3778
Additional Information:© 2015 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Article funded by SCOAP3. Received: July 25, 2015; Accepted: August 31, 2015; Published: September 21, 2015. We thank Mario Berta, Venkat Chandrasekaran, Bartek Czech, Patrick Hayden, Shaun Maguire, Alexander Maloney, Donald Marolf, Ingmar Saberi, and Adam Sheffer for pleasant discussions. M.W. acknowledges funding provided by the Simons Foundation and FQXi. N.B., H.O., and B.S. are supported in part by U.S. DOE grant DE-SC0011632 and by the Walter Burke Institute for Theoretical Physics (Burke Institute) at Caltech. The work of H.O. is also supported in part by the Simons Investigator Award, by the WPI Initiative of MEXT of Japan, and by JSPS Grant-in-Aid for Scientific Research C-26400240. N.B. is a DuBridge Fellow of the Burke Institute. S.N. is supported by a Stanford Graduate Fellowship. N.B. and B.S. thank the Stanford Institute for Theoretical Physics for hospitality. S.N., J.S., and M.W. thank the Burke Institute at Caltech for hospitality. H.O. thanks the hospitality of the Simons Foundation at the Simons Symposium on Quantum Entanglement.
Group:Walter Burke Institute for Theoretical Physics, Institute for Quantum Information and Matter
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Simons FoundationUNSPECIFIED
Foundational Questions Institute (FQXI)UNSPECIFIED
Department of Energy (DOE)DE-SC0011632
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Ministry of Education, Culture, Sports, Science and Technology (MEXT)UNSPECIFIED
Japan Society for the Promotion of Science (JSPS)C-26400240
Stanford UniversityUNSPECIFIED
Lee A. DuBridge FoundationUNSPECIFIED
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Issue or Number:9
Record Number:CaltechAUTHORS:20150616-154806338
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:58295
Deposited By: Joy Painter
Deposited On:16 Jun 2015 23:13
Last Modified:10 Nov 2021 22:02

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