Sharing Classical Secrets with Continuous-Variable Entanglement: Composable
Security and Network Coding Advantage

Secret sharing is a multiparty 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 bipartite quantum key distribution (QKD) and those that exploit multipartite 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 multipartite entanglement is typically challenging—one might well ask is there any virtue in pursuing multipartite 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 multipartite scheme outperforms the corresponding QKD-based method in the asymptotic and finite-size setting. Finally, we establish experimental parameters where the multipartite schemes outperform any possible QKD-based protocol. This is one of the first concrete compelling examples of multipartite 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.