Genuinely Multipartite Noncausality

Understand

The study of correlations with no definite causal order has revealed a rich structure emerging when more than two parties are involved.

• This motivates the consideration of multipartite "noncausal" correlations that cannot be realised even if noncausal resources are made available to a smaller number of parties.
• Here we formalise this notion: genuinely N-partite noncausal correlations are those that cannot be produced by grouping N parties into two or more subsets, where a causal order between the subsets exists.
• We prove that such correlations can be characterised as lying outside a polytope, whose vertices correspond to deterministic strategies and whose facets define what we call "2-causal" inequalities.