Holographic entropy relations

TL;DR

This paper introduces a geometric framework for deriving new holographic information measures, demonstrating its effectiveness by deriving tripartite information and extending it to multiple parties, applicable to static and dynamic geometries.

Contribution

The authors develop a surface-based method to derive multipartite information quantities in holography, independent of explicit entropy calculations, broadening understanding of entanglement structures.

Findings

Derived tripartite information using abstract surface manipulations.

Extended the framework to arbitrary numbers of parties.

Applicable to both static and dynamic bulk geometries.

Abstract

We develop a framework for the derivation of new information theoretic quantities which are natural from a holographic perspective. We demonstrate the utility of our techniques by deriving the tripartite information (the quantity associated to monogamy of mutual information) using a set of abstract arguments involving bulk extremal surfaces. Our arguments rely on formal manipulations of surfaces and not on local surgery or explicit computation of entropies through the holographic entanglement entropy prescriptions. As an application, we show how to derive a family of similar information quantities for an arbitrary number of parties. The present work establishes the foundation of a broader program that aims at the understanding of the entanglement structures of geometric states for an arbitrary number of parties. We stress that our method is completely democratic with respect to bulk geometries and is equally valid in static and dynamical situations. While rooted in holography, we expect that our construction will provide a useful characterization of multipartite correlations in quantum field theories.