No Bipartite-Nonlocal Causal Theory Can Explain Nature’s Correlations

We show that some tripartite quantum correlations are inexplicable by any causal theory involving bipartite nonclassical common causes and unlimited shared randomness. This constitutes a device-independent proof that nature’s nonlocality is fundamentally at least tripartite in every conceivable physical theory—no matter how exotic. To formalize this claim, we are compelled to substitute Svetlichny’s historical definition of genuine tripartite nonlocality with a novel theory-agnostic definition tied to the framework of local operations and shared randomness. A companion article by Coiteux-Roy et al. generalizes these concepts to any $N\ge 3$ number of parties, providing experimentally amenable device-independent inequality constraints along with quantum correlations violating them, thereby certifying that nature’s nonlocality must be boundlessly multipartite.

Figure 1

A tripartite distribution is genuinely tripartite nonlocal according to our definition if it cannot be realized by the above scenario, where the output of each player is determined by local operations (such as joint measurements) on (1) their input, (2) the three-way randomness, and (3) two-way GPT resources.

Figure 2

The inflation technique consists of duplicating and rearranging players, sources, and input distributions. Here we inflate the (nongenuinely tripartite-nonlocal) triangle scenario of Fig. 1 as to have the players play two parallel games ($\mathsf{Bell}$ and $\mathsf{same}$). It leads to a contradiction with the statistics of measurements on $|\mathrm{GHZ}⟩$, and therefore to the conclusion that the $|\mathrm{GHZ}⟩$ quantum state is a genuinely tripartite-nonlocal resource. The duplicated players constitute indistinguishable copies of the same abstract process, hence Alice, on input $X=\mathbf{0}$, could be playing either game ($A_1$ and $A_2$ must have the same behavior). The only condition on the random inputs is that they be independent from all of the sources. The figure represents a cut of a larger inflation of order 3, consisting of a triangle and a hexagon.