Tripartite information of highly entangled states

TL;DR

This paper explores the behavior of tripartite information in highly entangled states, proposing algorithms for local maxima and analyzing its role in quantum scrambling and holography.

Contribution

It introduces an algorithmic method to construct local maxima of tripartite information and classifies its values in perfect bipartite states, advancing understanding of entanglement measures.

Findings

Proposed an algorithm to build local maxima of I3 for any partitioning.

Classified I3 values for perfect bipartite states.

Suggested I3's average over permutations as a measure of scrambling.

Abstract

Holographic systems require monogamous mutual information for validity of semiclassical geometry. This is encoded by the sign of the tripartite information ($I3$). We investigate the behaviour of $I3$ for all partitionings of systems in states which are highly entangled in a multipartite or bipartite sense. In the case of multipartite entanglement we propose an algorithmic construction that we conjecture can be used to build local maxima of $I3$ for any partitioning. In case of bipartite entanglement we classify the possible values of $I3$ for perfect states and investigate, in some examples, the effect on its sign definiteness due to deformations of the states. Finally we comment on the proposal of using $I3$ as a parameter of scrambling, arguing that in general its average over qubits permutations could be a more sensible measure.