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Bulk locality and cooperative flows
High Energy Physics - Theory · Submitted 16 Aug 2018
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The explicit nature of the construction reveals that MMI is more deeply rooted in bulk locality than is the case for strong subadditivity.
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The abstract, sentence by sentence
We use the 'bit thread' formulation of holographic entanglement entropy to highlight the distinction between the universally-valid strong subadditivity and the more restrictive relation called monogamy of mutual information (MMI), known to hold for geometrical states (i.e. states of holographic theories with gravitational duals describing a classical bulk geometry). In particular, we provide a novel proof of MMI, using bit threads directly. To this end, we present an explicit geometrical construction of cooperative flows which we build out of disjoint thread bundles. We conjecture that our method applies in a wide class of configurations, including ones with non-trivial topology, causal structure, and time dependence. The explicit nature of the construction reveals that MMI is more deeply rooted in bulk locality than is the case for strong subadditivity.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We use the 'bit thread' formulation of holographic entanglement entropy to highlight the distinction between the universally-valid strong subadditivity and the more restrictive relation called monogamy of mutual information (MMI), known to hold for geometrical states (i.e. states of holographic theories with gravitational duals describing a classical bulk geometry). | background 0.82 | 0.43 | 0.12 | asserted 1.00 |
| s1 | In particular, we provide a novel proof of MMI, using bit threads directly. | contribution 0.94 | 0.96 | 0.16 | asserted 1.00 |
| s2 | To this end, we present an explicit geometrical construction of cooperative flows which we build out of disjoint thread bundles. | method 0.80 | 0.95 | 0.08 | asserted 1.00 |
| s3 | We conjecture that our method applies in a wide class of configurations, including ones with non-trivial topology, causal structure, and time dependence. | future work 0.74 | 0.31 | 0.07 | speculative 0.99 |
| s4 | The explicit nature of the construction reveals that MMI is more deeply rooted in bulk locality than is the case for strong subadditivity. | interpretation 0.99 | 0.81 | 0.75 | asserted 0.99 |
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The paper
Original abstract
We use the 'bit thread' formulation of holographic entanglement entropy to highlight the distinction between the universally-valid strong subadditivity and the more restrictive relation called monogamy of mutual information (MMI), known to hold for geometrical states (i.e. states of holographic theories with gravitational duals describing a classical bulk geometry). In particular, we provide a novel proof of MMI, using bit threads directly. To this end, we present an explicit geometrical construction of cooperative flows which we build out of disjoint thread bundles. We conjecture that our method applies in a wide class of configurations, including ones with non-trivial topology, causal structure, and time dependence. The explicit nature of the construction reveals that MMI is more deeply rooted in bulk locality than is the case for strong subadditivity.
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References
How the literature uses it
25 arXiv papers cite this in 37 sentences
Papers citing it · 27 sentences without a confident label
Cites it as support 1 paper
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The remarkable fact that all geometric states of holographic field theories necessarily satisfy this inequality [ref] then hints at some residual quantumness of the state (despite the bulk geometry itself being described by classical dynamics), perhaps even associated with bulk locality in this context [ref] , whose precise meaning would be illuminating to understand.
Holographic entropy relations · Introduction · 0.97
Cites it as background 8 papers
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Remember the flow-based proofs of the Araki-Lieb (AL) inequality, the subadditivity (SA) and the strong subadditivity (SSA) for the HEE [ref] , also the multiflow-based proof of the monogamy of the mutual information (MMI) [ref] .
Inequalities of Holographic Entanglement of Purification from Bit Threads · Relative homology and generalized HEE · 0.83
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This perspective is inspired by the so-called bit threads [ref] [For the recent developments of bit threads see e.g. [ref] .], which arise from the rephrasing of the RT formula for holographic entanglement entropy.
Holographic coarse-grained states and the necessity of perfect entanglement · Introduction · 0.88
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Bit threads have been used to study multipartite entanglement [ref] , holographic monogamy of mutual information [ref] , the hypergraph entropy cone [ref] , metric reconstruction [ref] , etc.
Lorentzian threads and generalized complexities · Introduction · 0.82
What it cites · 60 sentences without a confident label
Uses the method or tool of 1 paper
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This is manifested by utilizing a different geometrical prescription for holographic entanglement entropy, namely the “bit thread" formulation of Freedman and Headrick [ref] .
Bit threads and holographic entanglement · Introduction · 1.00
Compares with 4 papers
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We can now readily confirm that the RT-based geometric proof of MMI is then manifestly identical[ Note that our present argument based on cancelation of surfaces hinges on the fact that our `minimal surfaces' are one-dimensional; in higher dimensions one has to recourse to the more refined argument of [ref] . ] to the SSA proof of [ref] : for either option in the RHS of e:SAC, $S(AC)$ is canceled by two of the terms on the RHS of e:MMI, with the remaining terms equivalent to either SSA e:sumSSA, or its purification WM e:sumWM.
A holographic proof of the strong subadditivity of entanglement entropy · Setup · 0.80
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We can now readily confirm that the RT-based geometric proof of MMI is then manifestly identical[ Note that our present argument based on cancelation of surfaces hinges on the fact that our `minimal surfaces' are one-dimensional; in higher dimensions one has to recourse to the more refined argument of [ref] . ] to the SSA proof of [ref] : for either option in the RHS of e:SAC, $S(AC)$ is canceled by two of the terms on the RHS of e:MMI, with the remaining terms equivalent to either SSA e:sumSSA, or its purification WM e:sumWM.
Holographic Mutual Information is Monogamous · Setup · 0.80
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For example the bit thread proof of SSA [ref] used nesting in the sense that there exists a common maximizer flow for nested regions.
Bit threads and holographic entanglement · Discussion · 0.85
Cites as background 10 papers
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In general time-dependent situations, one can covariantize these prescriptions, which gives rise to the Hubeny-Rangamani-Takayanagi (HRT) prescription [ref] in terms of extremal surfaces $X$ which can also be recast into the Wall prescription [ref] in terms of `maximin' surfaces,[]
Maximin Surfaces, and the Strong Subadditivity of the Covariant Holographic Entanglement Entropy · Time dependence · 0.87
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In general time-dependent situations, one can covariantize these prescriptions, which gives rise to the Hubeny-Rangamani-Takayanagi (HRT) prescription [ref] in terms of extremal surfaces $X$ which can also be recast into the Wall prescription [ref] in terms of `maximin' surfaces,[]
A Covariant Holographic Entanglement Entropy Proposal · Time dependence · 0.87
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Entanglement wedge (first introduced in [ref] ) for a bulk region $X$ is the domain of dependence of the bulk homology region $r_X$ (part of a bulk Cauchy slice such that $∂ r__X = X - X$), or equivalently the set of spacelike-separated bulk points between $X$ and $X$.
Causality & holographic entanglement entropy · Time dependence · 0.98
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