Abstract
Bit threads, a dual description of the Ryu-Takyanagi formula for holographic entanglement entropy (EE), can be interpreted as a distillation of the quantum information to a collection of Bell pairs between different boundary regions. In this article we discuss a generalization to hyperthreads which can connect more than two boundary regions leading to a rich and diverse class of convex programs. By modeling the contributions of different species of hyperthreads to the EEs of perfect tensors we argue that this framework may be useful for helping us to begin to probe the multipartite entanglement of holographic systems. Furthermore, we demonstrate how this technology can potentially be used to understand holographic entropy cone inequalities and may provide an avenue to address issues of locking.
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S. Ryu and T. Takayanagi, Aspects of Holographic Entanglement Entropy, JHEP 08 (2006) 045 [hep-th/0605073] [INSPIRE].
M. Freedman and M. Headrick, Bit threads and holographic entanglement, Commun. Math. Phys. 352 (2017) 407 [arXiv:1604.00354] [INSPIRE].
M. Headrick and V.E. Hubeny, Riemannian and Lorentzian flow-cut theorems, Class. Quant. Grav. 35 (2018) 10 [arXiv:1710.09516] [INSPIRE].
N. Bao, S. Nezami, H. Ooguri, B. Stoica, J. Sully and M. Walter, The Holographic Entropy Cone, JHEP 09 (2015) 130 [arXiv:1505.07839] [INSPIRE].
V.E. Hubeny, M. Rangamani and M. Rota, The holographic entropy arrangement, Fortsch. Phys. 67 (2019) 1900011 [arXiv:1812.08133] [INSPIRE].
V.E. Hubeny, M. Rangamani and M. Rota, Holographic entropy relations, Fortsch. Phys. 66 (2018) 1800067 [arXiv:1808.07871] [INSPIRE].
S. Hernández Cuenca, Holographic entropy cone for five regions, Phys. Rev. D 100 (2019) 026004 [arXiv:1903.09148] [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].
S.X. Cui, P. Hayden, T. He, M. Headrick, B. Stoica and M. Walter, Bit Threads and Holographic Monogamy, Commun. Math. Phys. 376 (2019) 609 [arXiv:1808.05234] [INSPIRE].
D. Avis and S. Hernández-Cuenca, The Six-Party Holographic Entropy Cone, work in progress (2022).
M. Fadel and S. Hernández-Cuenca, Symmetrized holographic entropy cone, Phys. Rev. D 105 (2022) 086008 [arXiv:2112.03862] [INSPIRE].
D. Avis and S. Hernández-Cuenca, On the foundations and extremal structure of the holographic entropy cone, arXiv:2102.07535 [INSPIRE].
T. He, V.E. Hubeny and M. Rangamani, Superbalance of Holographic Entropy Inequalities, JHEP 07 (2020) 245 [arXiv:2002.04558] [INSPIRE].
S. Hernández-Cuenca, V.E. Hubeny and M. Rota, The holographic entropy cone from marginal independence, arXiv:2204.00075 [INSPIRE].
B. Czech and S. Shuai, Holographic Cone of Average Entropies, arXiv:2112.00763 [INSPIRE].
T. He, M. Headrick and V.E. Hubeny, Holographic Entropy Relations Repackaged, JHEP 10 (2019) 118 [arXiv:1905.06985] [INSPIRE].
S. Boyd, Convex optimization, Cambridge University Press, Cambridge, U.K. (2004).
M. Headrick, J. Held and J. Herman, Crossing versus locking: Bit threads and continuum multiflows, arXiv:2008.03197 [INSPIRE].
J. Harper, Hyperthreads in holographic spacetimes, JHEP 09 (2021) 118 [arXiv:2107.10276] [INSPIRE].
A. Frank, A.V. Karzanov and A. Sebo, On integer multiflow maximization, SIAM J. Discr. Math. 10 (1997) 158.
C. Akers and P. Rath, Entanglement Wedge Cross Sections Require Tripartite Entanglement, JHEP 04 (2020) 208 [arXiv:1911.07852] [INSPIRE].
P. Hayden, O. Parrikar and J. Sorce, The Markov gap for geometric reflected entropy, JHEP 10 (2021) 047 [arXiv:2107.00009] [INSPIRE].
T. Takayanagi and K. Umemoto, Entanglement of purification through holographic duality, Nature Phys. 14 (2018) 573 [arXiv:1708.09393] [INSPIRE].
P. Nguyen, T. Devakul, M.G. Halbasch, M.P. Zaletel and B. Swingle, Entanglement of purification: from spin chains to holography, JHEP 01 (2018) 098 [arXiv:1709.07424] [INSPIRE].
S. Dutta and T. Faulkner, A canonical purification for the entanglement wedge cross-section, JHEP 03 (2021) 178 [arXiv:1905.00577] [INSPIRE].
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Harper, J. Perfect tensor hyperthreads. J. High Energ. Phys. 2022, 239 (2022). https://doi.org/10.1007/JHEP09(2022)239
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DOI: https://doi.org/10.1007/JHEP09(2022)239