Fig. 1: Distributed computation in a CCP scenario.

a A central agent allocates resources among a network of n users who independently produce outcomes to solve a collective task. Each user i receives y_i and a subset x_i of the variables \(\left\{{x}_{1},\cdots \ ,{x}_{n}\right\}\) according to some underlying causal structure indicated by the shaded pink region. Each user processes their input data along with shared correlations and broadcast a one-bit message m_i to all others before they compute a function f(x₁, …, x_n, y₁, …, y_n). When allowing for quantum resources, shared quantum correlations that violate a Bell-like inequality bounding the corresponding NLHV model provide an advantage in the probability of success of the task over its classical counterpart. b Causal structure of the three-party GYNI scenario^41,49 experimentally investigated. The input of each party x_i is communicated to its neighbour to the right (or alternatively, to the left). The variable λ stands for pre-shared (classical) correlations shared among the parties and used to produces respective outcomes, a_i. c Causal structure of Svetlichny’s scenario⁴⁰ as discussed in Supplementary Methods.