The Symmetrized Holographic Entropy Cone

Abstract

The holographic entropy cone (HEC) characterizes the entanglement structure of quantum states which admit geometric bulk duals in holography. Due to its intrinsic complexity, to date it has only been possible to completely characterize the HEC for at most $n=5$ numbers of parties. For larger $n$, our knowledge of the HEC falls short of incomplete: almost nothing is known about its extremal elements. Here, we introduce a symmetrization procedure that projects the HEC onto a natural lower dimensional subspace. Upon symmetrization, we are able to deduce properties that its extremal structure exhibits for general $n$. Further, by applying this symmetrization to the quantum entropy cone, we are able to quantify the typicality of holographic entropies, which we find to be exponentially rare quantum entropies in the number of parties.

arXiv commentComments are welcome!

References in corpus (27)

• The Large N Limit of Superconformal Field Theories and Supergravity
• Holographic Derivation of Entanglement Entropy from AdS/CFT
• The World as a Hologram
• A Covariant Holographic Entanglement Entropy Proposal
• Building up spacetime with quantum entanglement
• Quantum Extremal Surfaces: Holographic Entanglement Entropy beyond the Classical Regime
• Quantum corrections to holographic entanglement entropy
• Dimensional Reduction in Quantum Gravity
• Maximin Surfaces, and the Strong Subadditivity of the Covariant Holographic Entanglement Entropy
• Holographic Mutual Information is Monogamous
• A holographic proof of the strong subadditivity of entanglement entropy
• Detecting non-locality in multipartite quantum systems with two-body correlation functions
• The Holographic Entropy Cone
• The Holographic Entropy Cone for Five Regions
• Multipartite Entanglement in Stabilizer Tensor Networks
• Holographic entropy relations
• The holographic entropy arrangement
• Holographic Entropy Relations Repackaged
• Bounding the set of classical correlations of a many-body system
• Quantum Extremal Surfaces and the Holographic Entropy Cone
• Superbalance of Holographic Entropy Inequalities
• On the foundations and extremal structure of the holographic entropy cone
• The Quantum Entropy Cone of Hypergraphs
• Holographic Cone of Average Entropies
• Hypergraph min-cuts from quantum entropies
• Topological Link Models of Multipartite Entanglement
• A Gap Between the Hypergraph and Stabilizer Entropy Cones

Cited by in corpus (19)

• On the foundations and extremal structure of the holographic entropy cone
• A holographic inequality for $N=7$ regions
• Holographic Entropy Inequalities and Multipartite Entanglement
• The holographic entropy cone from marginal independence
• Holographic Cone of Average Entropies
• Two infinite families of facets of the holographic entropy cone
• Perfect tensor hyperthreads
• Testing holographic entropy inequalities in 2+1 dimensions
• Properties of the contraction map for holographic entanglement entropy inequalities
• More on the upper bound of holographic n-partite information
• Towards a complete classification of holographic entropy inequalities
• A framework for generalizing toric inequalities for holographic entanglement entropy
• Beyond the Holographic Entropy Cone via Cycle Flows
• Deriving three-outcome permutationally invariant Bell inequalities
• Purely GHZ-like entanglement is forbidden in holography
• On the completeness of contraction map proof method for holographic entropy inequalities
• Discrete Bulk Reconstruction
• Upper bound of holographic entanglement entropy combinations
• Exploring the holographic entropy cone via reinforcement learning