Holographic Entropy Inequalities and Multipartite Entanglement

Abstract

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 simpler ones which share interestingly rigid structures. By performing a systematic search over some of these structures, we are able to discover more than 300 novel entropy inequalities for six parties, thereby demonstrating that these recastings provide a fruitful generating technique for uncovering new holographic entropy inequalities. In attempting to interpret the corresponding sign-definite quantities as correlation measures, we also obtain a no-go result: the superbalance property of holographic entropy inequalities turns out to preclude them from being monotonic under partial tracing. In the process, we also comment on the geometrical significance of multipartite information quantities and present various structural relations amongst them.

v1: 40 pages, 384 inequalities. v2: 1877 inequalities (w/ numbering distinct from v1); new tables in App. C; link to living repository added

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Cited by in corpus (14)

• Holographic Entropy Inequalities and Multipartite Entanglement
• Two infinite families of facets of the holographic entropy cone
• Testing holographic entropy inequalities in 2+1 dimensions
• Towards a complete classification of holographic entropy inequalities
• Reflected multi-entropy and its holographic dual
• A framework for generalizing toric inequalities for holographic entanglement entropy
• Algorithmic construction of SSA-compatible extreme rays of the subadditivity cone and the $\mathsf{N}=6$ solution
• Purely GHZ-like entanglement is forbidden in holography
• On the completeness of contraction map proof method for holographic entropy inequalities
• Holographic multipartite entanglement structures in IR modified geometries
• Revisiting holographic codes with fractal-like boundary erasures
• Upper bound of holographic entanglement entropy combinations
• Topological entanglement entropy meets holographic entropy inequalities
• Exploring the holographic entropy cone via reinforcement learning