Related papers: Bit threads on hypergraphs
Significant work has gone into determining the minimal set of entropy inequalities that determine the holographic entropy cone. Holographic systems with three or more parties have been shown to obey additional inequalities that generic…
This work deals with the scattering entropy of quantum graphs in many different circumstances. We first consider the case of the Shannon entropy and then the R\'enyi and Tsallis entropies, which are more adequate to study distinct…
Hypergraphs are a generalization of graphs in which edges can connect any number of vertices. They allow the modeling of complex networks with higher-order interactions, and their spectral theory studies the qualitative properties that can…
Hypergraphs are a useful abstraction for modeling multiway relationships in data, and hypergraph clustering is the task of detecting groups of closely related nodes in such data. Graph clustering has been studied extensively, and there are…
Unsupervised hashing is important for indexing huge image or video collections without having expensive annotations available. Hashing aims to learn short binary codes for compact storage and efficient semantic retrieval. We propose an…
The purpose of this report is to provide a framework for defining phase transition processes in two dimensional holographic superconductors, and to illustrate how they are useful to be described by holographic entanglement entropy. We study…
Starting from the entanglement wedge of a multipartite mixed state we describe a purification procedure which involves the gluing of several copies. The resulting geometry has non-trivial topology and a single oriented boundary for each…
We apply machine learning to understand fundamental aspects of holographic duality, specifically the entropies obtained from the apparent and event horizon areas. We show that simple features of only the time series of the pressure…
The entanglement of purification (EoP), which measures the classical correlations and entanglement of a given mixed state, has been conjectured to be dual to the area of the minimal cross section of the entanglement wedge in holography.…
In AdS/CFT, the entanglement wedge EW$(B)$ is the portion of the bulk geometry that can be reconstructed from a boundary region $B$; in other words, EW$(B)$ is the hologram of $B$. We extend this notion to arbitrary spacetimes. Given any…
Hypergraphs allow modeling problems with multi-way high-order relationships. However, the computational cost of most existing hypergraph-based algorithms can be heavily dependent upon the input hypergraph sizes. To address the…
Recently, the reflected entropy is proposed in holographic approach to describe the entanglement of a bipartite quantum system in a mixed state, which is identified as the area of the reflected minimal surface inside the entanglement wedge.…
Recently, a holographic computation of the entanglement entropy in conformal field theories has been proposed via the AdS/CFT correspondence. One of the most important properties of the entanglement entropy is known as the strong…
A network can be analyzed at different topological scales, ranging from single nodes to motifs, communities, up to the complete structure. We propose a novel intermediate-level topological analysis that considers non-overlapping subgraphs…
We study and prove properties of the minimax formulation of the HRT holographic entanglement entropy formula, which involves finding the maximal-area surface on a timelike hypersurface, or time-sheet, and then minimizing over the choice of…
In this note we show that the holographic entanglement entropy inequalities that hold for constant time slices are also valid for large regions and times in covariant spacetimes containing collapsing black branes, where the leading part of…
The embedding of finite metrics in $\ell_1$ has become a fundamental tool for both combinatorial optimization and large-scale data analysis. One important application is to network flow problems in which there is close relation between…
We provide a derivation of holographic entanglement entropy for spherical entangling surfaces. Our construction relies on conformally mapping the boundary CFT to a hyperbolic geometry and observing that the vacuum state is mapped to a…
Even though little is known about the quantum entropy cone for $N\geq4$ subsystems, holographic techniques allow one to get a handle on the subspace of entropy vectors corresponding to states with gravity duals. For static spacetimes and…
We expand the results of arXiv:1105.5165, where a holographic description of a conformal field theory defined on a manifold with boundaries (so called BCFT) was proposed, based on AdS/CFT. We construct gravity duals of conformal field…