Holographic Entropy Inequalities and Multipartite Entanglement

TL;DR

This paper introduces a new method for deriving holographic entropy inequalities by grouping terms into multipartite information quantities, leading to over 300 new inequalities and insights into their structural and geometric properties.

Contribution

The paper develops a systematic approach to discover new holographic entropy inequalities using multipartite information structures, significantly expanding the known set of inequalities.

Findings

Discovered over 300 new entropy inequalities for six parties.

Revealed structural and geometric properties of multipartite information quantities.

Showed that holographic entropy inequalities cannot be monotonic under partial tracing.

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.