On genuine multipartite entanglement signals

TL;DR

This paper introduces a general method to construct signals of genuine multipartite entanglement using lower-partite invariants and M"obius inversion, unifying many existing approaches.

Contribution

It provides a unified framework for constructing multipartite entanglement signals from lower-partite invariants, leveraging M"obius inversion on the partition lattice.

Findings

Many existing multipartite entanglement signals fit this framework

The construction can extract signals from non-symmetric multi-invariants

The approach unifies various entanglement detection methods

Abstract

We give a general construction of genuinely multipartite entanglement signals from families of lower-partite symmetric local-unitary invariants satisfying a natural compatibility condition. M\"obius inversion on the partition lattice plays a key role in this construction. We show that many examples of multipartite entanglement signals considered in the literature fit naturally into this framework. We also explain how the genuinely multipartite signal can be extracted from a general, not necessarily symmetric, multi-invariant.