Related papers: A holographic inequality for $N=7$ regions
In holographic duality, if a boundary state has a geometric description that realizes the Ryu-Takayanagi proposal then its entanglement entropies must obey certain inequalities that together define the so-called holographic entropy cone. 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 perform a holographic calculation of the Entanglement R\'enyi entropy $S_q(\mu,\lambda)$, for spherical entangling surfaces in boundary CFT's with Einstein-Gauss-Bonnet-Maxwell holographic gravitational duals. We find that for…
We initiate a systematic enumeration and classification of entropy inequalities satisfied by the Ryu-Takayanagi formula for conformal field theory states with smooth holographic dual geometries. For 2, 3, and 4 regions, we prove that the…
The domain of allowed von Neumann entropies of a holographic field theory carves out a polyhedral cone -- the holographic entropy cone -- in entropy space. Such polyhedral cones are characterized by their extreme rays. For an arbitrary…
We extend our studies of holographic entropy inequalities to gapped phases of matter. For any number of regions, we determine the linear entropy inequalities satisfied by systems in which the entanglement entropy satisfies an exact area…
We study the holographic dual of a two parameter family of quantities known as the $\alpha$-$z$ divergences. Many familiar information theoretic quantities occur within this family, including the relative entropy, fidelity, and collision…
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…
Tensor networks implementing quantum error correcting codes have recently been used to construct toy models of holographic duality explicitly realizing some of the more puzzling features of the AdS/CFT correspondence. These models reproduce…
We study holographic entropy inequalities and their structural properties by making use of a judicious grouping of terms into certain multipartite information quantities. This allows us to recast cumbersome entropic expressions into much…
We describe an explicit mechanism for the emergence of a dynamical holographic bulk from the structure of entanglement in a quantum state. We start with a generic system in complete isolation, assuming it has a classical limit involving…
The holographic bound asserts that the entropy $S$ of a system is bounded from above by a quarter of the area ${\cal A}$ of a circumscribing surface measured in Planck areas: $S\leq {\cal A}/4{\ell^2_P}$. This bound is widely regarded a…
Random tensor networks provide useful models that incorporate various important features of holographic duality. A tensor network is usually defined for a fixed graph geometry specified by the connection of tensors. In this paper, we…
We present a graphical method for proving holographic entanglement entropy inequalities (HEIs) in general multipartite systems. By introducing a geometric representation of the entanglement structure, we develop a systematic approach that…
We reformulate entanglement wedge reconstruction in the language of operator-algebra quantum error correction with infinite-dimensional physical and code Hilbert spaces. Von Neumann algebras are used to characterize observables in a…
Quantum states with geometric duals are known to satisfy a stricter set of entropy inequalities than those obeyed by general quantum systems. The set of allowed entropies derived using the Ryu-Takayanagi (RT) formula defines the Holographic…
Quantities computed by minimal cuts, such as entanglement entropies achievable by the Ryu-Takayanagi proposal in the AdS/CFT correspondence, are constrained by linear inequalities. We prove a previously conjectured property of all such…
Recently, a novel formula for computing entropy in theories coupled to semi-classical gravity has been devised. Using this so-called island formula the entropy of semi-classical black holes follows a Page curve. Here, we study the relation…
Subregion duality in AdS/CFT implies certain constraints on the geometry: entanglement wedges must contain causal wedges, and nested boundary regions must have nested entanglement wedges. We elucidate the logical connections between these…
In this letter we define a natural generalization of the von Neumann entropy to multiple parties that is symmetric with respect to all the parties. We call this measure multi-entropy. We show that for conformal field theories with…