Abstract
We explore the structure of holographic entropy relations (associated with ‘information quantities’ given by a linear combination of entanglement entropies of spatial sub-partitions of a CFT state with geometric bulk dual). Such entropy relations can be recast in multiple ways, some of which have significant advantages. Motivated by the already-noted simplification of entropy relations when recast in terms of multipartite information, we explore additional simplifications when recast in a new basis, which we dub the K-basis, constructed from perfect tensor structures. For the fundamental information quantities such a recasting is surprisingly compact, in part due to the interesting fact that entropy vectors associated to perfect tensors are in fact extreme rays in the holographic entropy cone (as well as the full quantum entropy cone). More importantly, we prove that all holographic entropy inequalities have positive coefficients when expressed in the K-basis, underlying the key advantage over the entropy basis or the multipartite information basis.
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References
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett.96 (2006) 181602 [hep-th/0603001] [INSPIRE].
V.E. Hubeny, M. Rangamani and T. Takayanagi, A Covariant holographic entanglement entropy proposal, JHEP07 (2007) 062 [arXiv:0705.0016] [INSPIRE].
M. Van Raamsdonk, Building up spacetime with quantum entanglement, Gen. Rel. Grav.42 (2010) 2323 [arXiv:1005.3035] [INSPIRE].
J. Maldacena and L. Susskind, Cool horizons for entangled black holes, Fortsch. Phys.61 (2013) 781 [arXiv:1306.0533] [INSPIRE].
M. Rangamani and T. Takayanagi, Holographic Entanglement Entropy, Lect. Notes Phys.931 (2017) 1 [arXiv:1609.01287] [INSPIRE].
E. Witten, APS Medal for Exceptional Achievement in Research: Invited article on entanglement properties of quantum field theory, Rev. Mod. Phys.90 (2018) 045003 [arXiv:1803.04993] [INSPIRE].
M. Headrick and T. Takayanagi, A Holographic proof of the strong subadditivity of entanglement entropy, Phys. Rev.D 76 (2007) 106013 [arXiv:0704.3719] [INSPIRE].
P. Hayden, M. Headrick and A. Maloney, Holographic Mutual Information is Monogamous, Phys. Rev.D 87 (2013) 046003 [arXiv:1107.2940] [INSPIRE].
A.C. Wall, Maximin Surfaces and the Strong Subadditivity of the Covariant Holographic Entanglement Entropy, Class. Quant. Grav.31 (2014) 225007 [arXiv:1211.3494] [INSPIRE].
E.H. Lieb and M.B. Ruskai, Proof of the strong subadditivity of quantum-mechanical entropy, J. Math. Phys.14 (1973) 1938 [INSPIRE].
V.E. Hubeny, Bulk locality and cooperative flows, JHEP12 (2018) 068 [arXiv:1808.05313] [INSPIRE].
S.X. Cui, P. Hayden, T. He, M. Headrick, B. Stoica and M. Walter, Bit Threads and Holographic Monogamy, arXiv:1808.05234 [INSPIRE].
M. Freedman and M. Headrick, Bit threads and holographic entanglement, Commun. Math. Phys.352 (2017) 407 [arXiv:1604.00354] [INSPIRE].
N. Bao, S. Nezami, H. Ooguri, B. Stoica, J. Sully and M. Walter, The Holographic Entropy Cone, JHEP09 (2015) 130 [arXiv:1505.07839] [INSPIRE].
V.E. Hubeny, M. Rangamani and M. Rota, Holographic entropy relations, Fortsch. Phys.66 (2018) 1800067 [arXiv:1808.07871] [INSPIRE].
V.E. Hubeny, M. Rangamani and M. Rota, The holographic entropy arrangement, Fortsch. Phys.67 (2019) 1900011 [arXiv:1812.08133] [INSPIRE].
S. Hernández Cuenca, Holographic entropy cone for five regions, Phys. Rev.D 100 (2019) 026004 [arXiv:1903.09148] [INSPIRE].
D. Marolf, M. Rota and J. Wien, Handlebody phases and the polyhedrality of the holographic entropy cone, JHEP10 (2017) 069 [arXiv:1705.10736] [INSPIRE].
H. Maxfield, S. Ross and B. Way, Holographic partition functions and phases for higher genus Riemann surfaces, Class. Quant. Grav.33 (2016) 125018 [arXiv:1601.00980] [INSPIRE].
S. Hernández Cuenca, V.E. Hubeny, M. Rangamani and M. Rota, to appear.
P. Hayden, S. Nezami, X.-L. Qi, N. Thomas, M. Walter and Z. Yang, Holographic duality from random tensor networks, JHEP11 (2016) 009 [arXiv:1601.01694] [INSPIRE].
W. Helwig, W. Cui, A. Riera, J.I. Latorre and H.-K. Lo, Absolute Maximal Entanglement and Quantum Secret Sharing, Phys. Rev.A 86 (2012) 052335 [arXiv:1204.2289] [INSPIRE].
D.N. Page, Information in black hole radiation, Phys. Rev. Lett.71 (1993) 3743 [hep-th/9306083] [INSPIRE].
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ArXiv ePrint: 1905.06985
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He, T., Headrick, M. & Hubeny, V.E. Holographic entropy relations repackaged. J. High Energ. Phys. 2019, 118 (2019). https://doi.org/10.1007/JHEP10(2019)118
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DOI: https://doi.org/10.1007/JHEP10(2019)118