Violation of Bell's inequalities in uniform random graphs

Abstract

We demonstrate that quantum correlations can emerge from the statistical correlations of random discrete models, without an a priori assumption that the random models are quantum mechanical in nature, that is without considering superpositions of the random structures. We investigate the correlations between the number of neighbors(degree) for pairs of vertices in Erdos-Renyi uniform random graphs. We use the joint probabilities for the appearance of degree numbers between the vertices in the pairs, in order to calculate the respective Bell's inequalities. We find that the inequalities are violated for sparse random graphs with ratio of edges over vertices $R<2$, signifying the emergence of quantum correlations for these random structures. The quantum correlations persist independently of the graph size or the geodesic distance between the correlated vertices. For $R>2$, as the graph becomes denser by adding more edges between its vertices, the Bell's inequalities are satisfied and the quantum correlations disappear. Relations to our previous works concerning the emergence of spacetime and its geometrical properties from uniform random graphs, are also briefly discussed.