{"arxiv_id":"1808.05313","incoming":{"papers":25,"sentences":37,"groups":[{"kind":"supports_this_paper","label":"Cites it as support","papers":1,"sentences":1,"quotes":[{"arxiv_id":"1808.07871","title":"Holographic entropy relations","url":"/paper/1808.07871","section":"Introduction","sentence":"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.","intent_p":0.97,"contests_p":null}]},{"kind":"background","label":"Cites it as background","papers":8,"sentences":9,"quotes":[{"arxiv_id":"1912.00557","title":"Inequalities of Holographic Entanglement of Purification from Bit Threads","url":"/paper/1912.00557","section":"Relative homology and generalized HEE","sentence":"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] .","intent_p":0.83,"contests_p":null},{"arxiv_id":"2312.14498","title":"Holographic coarse-grained states and the necessity of perfect entanglement","url":"/paper/2312.14498","section":"Introduction","sentence":"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.","intent_p":0.88,"contests_p":null},{"arxiv_id":"2312.10606","title":"Lorentzian threads and generalized complexities","url":"/paper/2312.10606","section":"Introduction","sentence":"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.","intent_p":0.82,"contests_p":null},{"arxiv_id":"2403.13283","title":"Properties of the contraction map for holographic entanglement entropy inequalities","url":"/paper/2403.13283","section":"Introduction","sentence":"Further work towards characterizing holographic entanglement includes the study of bit threads [ref] , the connection to quantum marginal independence problems [ref] , generalizations to other measures of holographic entanglement [ref] , and extensions of the tools and proof techniques beyond the holographic setting [ref] .","intent_p":0.99,"contests_p":null},{"arxiv_id":"2203.07117","title":"Snowmass white paper: Quantum information in quantum field theory and quantum gravity","url":"/paper/2203.07117","section":"Entanglement in holography, gravity, and string theory","sentence":"The so-called holographic entropy cone defined by these inequalities has been extensively studied [ref] .","intent_p":0.87,"contests_p":null}]}],"unlabelled_sentences":27},"outgoing":{"papers":30,"sentences":75,"groups":[{"kind":"method_or_tool","label":"Uses the method or tool of","papers":1,"sentences":1,"quotes":[{"arxiv_id":"1604.00354","title":"Bit threads and holographic entanglement","url":"/paper/1604.00354","section":"Introduction","sentence":"This is manifested by utilizing a different geometrical prescription for holographic entanglement entropy, namely the “bit thread\" formulation of Freedman and Headrick [ref] .","intent_p":1.0,"contests_p":null}]},{"kind":"comparison","label":"Compares with","papers":4,"sentences":4,"quotes":[{"arxiv_id":"0704.3719","title":"A holographic proof of the strong subadditivity of entanglement entropy","url":"/paper/0704.3719","section":"Setup","sentence":"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.","intent_p":0.8,"contests_p":null},{"arxiv_id":"1107.2940","title":"Holographic Mutual Information is Monogamous","url":"/paper/1107.2940","section":"Setup","sentence":"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.","intent_p":0.8,"contests_p":null},{"arxiv_id":"1604.00354","title":"Bit threads and holographic entanglement","url":"/paper/1604.00354","section":"Discussion","sentence":"For example the bit thread proof of SSA [ref] used nesting in the sense that there exists a common maximizer flow for nested regions.","intent_p":0.85,"contests_p":null},{"arxiv_id":"1708.09393","title":"Holographic Entanglement of Purification","url":"/paper/1708.09393","section":"Discussion","sentence":"In particular, our constructions are rather reminiscent of the holographic entanglement of purification proposed in [ref] .","intent_p":0.97,"contests_p":null}]},{"kind":"background","label":"Cites as background","papers":10,"sentences":10,"quotes":[{"arxiv_id":"1211.3494","title":"Maximin Surfaces, and the Strong Subadditivity of the Covariant Holographic Entanglement Entropy","url":"/paper/1211.3494","section":"Time dependence","sentence":"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,[]","intent_p":0.87,"contests_p":null},{"arxiv_id":"0705.0016","title":"A Covariant Holographic Entanglement Entropy Proposal","url":"/paper/0705.0016","section":"Time dependence","sentence":"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,[]","intent_p":0.87,"contests_p":null},{"arxiv_id":"1408.6300","title":"Causality & holographic entanglement entropy","url":"/paper/1408.6300","section":"Time dependence","sentence":"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 $X$.","intent_p":0.98,"contests_p":null},{"arxiv_id":"1604.00354","title":"Bit threads and holographic entanglement","url":"/paper/1604.00354","section":"Discussion","sentence":"Originally the bit thread prescription of [ref] was formulated with the explicit goal to provide an alternate prescription for entanglement entropy.","intent_p":0.99,"contests_p":null},{"arxiv_id":"1505.07839","title":"The Holographic Entropy Cone","url":"/paper/1505.07839","section":"Introduction","sentence":"Refining the partition into several subsystems $A$, $B$, etc., we can consider general constraints on the respective entanglement entropies.[ It is known that even in the restricted context of holography [ref] , there are in fact infinitely many such relations if we allow arbitrary number of partitions, though the complete set has hitherto remained elusive. ] For example, among particularly useful relations are sub-additivity (SA), strong sub-additivity (SSA) and its cousin (related by purification) weak monotonicity (WM), and the above-mentioned monogamy of mutual information (MMI), which can respectively be expressed as:","intent_p":0.94,"contests_p":null}]}],"unlabelled_sentences":60},"claims":[],"thresholds":{"intent_p":0.8,"supports_p":0.95,"contests_p":0.7},"method":"Citing sentences come from each paper's LaTeX source; every \\cite marks the sentence and the works it cites. Pith's classifier typed each sentence. A label is shown at intent probability 0.8 or more (0.95 for support), a contest at 0.7 or more. Measured accuracy against two blind model families is at https://pith.science/accuracy. The quoted sentences are the citing authors' own.","held_up":null,"_links":{"html":"https://pith.science/paper/1808.05313"}}