Heuristic for estimation of multiqubit genuine multipartite entanglement

TL;DR

This paper introduces a simple heuristic for estimating the genuine multipartite entanglement in multiqubit states, which is computationally easier and closely approximates existing bounds, with applications to the driven Dicke model.

Contribution

The paper proposes a new heuristic method for estimating GM-concurrence that is easier to compute and closely matches standard bounds, with a novel application to the driven Dicke model.

Findings

Heuristic estimates are close to standard lower bounds on GM-concurrence.

The method simplifies the computation of GM-entanglement in multiqubit states.

First characterization of GM-entanglement in steady states of the driven Dicke model.

Abstract

For every N-qubit density matrix written in the computational basis, an associated "X-density matrix" can be obtained by vanishing all entries out of the main- and anti-diagonals. It is very simple to compute the genuine multipartite (GM) concurrence of this associated N-qubit X-state, which, moreover, lower bounds the GM-concurrence of the original (non-X) state. In this paper, we rely on these facts to introduce and benchmark a heuristic for estimating the GM-concurrence of an arbitrary multiqubit mixed state. By explicitly considering two classes of mixed states, we illustrate that our estimates are usually very close to the standard lower bound on the GM-concurrence, being significantly easier to compute. In addition, while evaluating the performance of our proposed heuristic, we provide the first characterization of GM-entanglement in the steady states of the driven Dicke model at zero temperature.