Genuine multiparticle entanglement of permutationally invariant states

TL;DR

This paper introduces a polynomial-time method for detecting genuine multiparticle entanglement in permutationally invariant states, significantly improving existing criteria and applicable to up to ten qubits.

Contribution

It presents a scalable approach using PPT mixtures to characterize genuine multiparticle entanglement in permutationally invariant states, including three-qubit cases.

Findings

Evaluation scales polynomially with particle number

Method is practical for up to ten qubits

Improves upon existing entanglement criteria

Abstract

We consider the problem of characterizing genuine multiparticle entanglement for permutationally invariant states using the approach of PPT mixtures. We show that the evaluation of this necessary biseparability criterion scales polynomially with the number of particles. In practice, it can be evaluated easily up to ten qubits and improves existing criteria significantly. Finally, we show that our approach solves the problem of characterizing genuine multiparticle entanglement for permutationally invariant three-qubit states.