Genuinely Multipartite Noncausality

TL;DR

This paper formalizes and characterizes genuinely multipartite noncausal correlations, revealing their structure, inequalities, and occurrence within the process matrix framework, advancing understanding of quantum correlations without a definite causal order.

Contribution

It introduces a formal definition of genuinely multipartite noncausality, characterizes these correlations via polytopes and inequalities, and explores their presence in the process matrix formalism.

Findings

Genuinely multipartite noncausal correlations are outside a specific polytope.

Certain inequalities (2-causal inequalities) define the boundaries of these correlations.

Some genuinely multipartite noncausal correlations are found within the process matrix formalism.

Abstract

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. We show that genuinely multipartite noncausal correlations arise within the process matrix formalism, where quantum mechanics holds locally but no global causal structure is assumed, although for some inequalities no violation was found. We further introduce two refined definitions that allow one to quantify, in different ways, to what extent noncausal correlations correspond to a genuinely multipartite resource.