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Secret sharing is a multi-party cryptographic primitive that can be appliedto a network of partially distrustful parties for encrypting data that is bothsensitive (it must remain secure) and important (it must not be lost ordestroyed). When sharing classical secrets (as opposed to quantum states), onecan distinguish between protocols that leverage bi-partite quantum keydistribution (QKD) and those that exploit multi-partite entanglement. Thelatter class are known to be vulnerable to so-called participant attacks and,while progress has been made recently, there is currently no analysis thatquantifies their performance in the composable, finite-size regime which hasbecome the gold standard for QKD security. Given this - and the fact thatdistributing multi-partite entanglement is typically challenging - one mightwell ask: Is there any virtue in pursuing multi-partite entanglement basedschemes? Here, we answer this question in the affirmative for a class of secretsharing protocols based on continuous variable graph states. We establishsecurity in a composable framework and identify a network topology,specifically a bottleneck network of lossy channels, and parameter regimeswithin the reach of present day experiments for which a multi-partite schemeoutperforms the corresponding QKD based method in the asymptotic andfinite-size setting. Finally, we establish experimental parameters where themulti-partite schemes outperform any possible QKD based protocol. This one ofthe first concrete compelling examples of multi-partite entangled resourcesachieving a genuine advantage over point-to-point protocols for quantumcommunication and represents a rigorous, operational benchmark to assess theusefulness of such resources.

Sharing classical secrets with continuous-variable entanglement: Composable security and network coding advantage