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.Comment: 19 pages, 5 figure