  Secret sharing is a multi-party cryptographic primitive that can be applied
to a network of partially distrustful parties for encrypting data that is both
sensitive (it must remain secure) and important (it must not be lost or
destroyed). When sharing classical secrets (as opposed to quantum states), one
can distinguish between protocols that leverage bi-partite quantum key
distribution (QKD) and those that exploit multi-partite entanglement. The
latter class are known to be vulnerable to so-called participant attacks and,
while progress has been made recently, there is currently no analysis that
quantifies their performance in the composable, finite-size regime which has
become the gold standard for QKD security. Given this -- and the fact that
distributing multi-partite entanglement is typically challenging -- one might
well ask: Is there is any virtue in pursuing multi-partite entanglement based
schemes? Here, we answer this question in the affirmative for a class of secret
sharing protocols based on continuous variable graph states. We establish
security in a composable framework and identify a network topology,
specifically a bottleneck network of lossy channels, and parameter regimes
within the reach of present day experiments for which a multi-partite scheme
outperforms the corresponding QKD based method in the asymptotic and
finite-size setting. Finally, we establish experimental parameters where the
multi-partite schemes outperform any possible QKD based protocol. This one of
the first concrete compelling examples of multi-partite entangled resources
achieving a genuine advantage over point-to-point protocols for quantum
communication and represents a rigorous, operational benchmark to assess the
usefulness of such resources.
