Closing the problem of which causal structures of up to six total nodes have a classical-quantum gap
This work resolves a foundational question in quantum mechanics about the existence of non-classical correlations in small causal structures, which is incremental but important for understanding quantum foundations.
The paper tackled the open problem of whether a specific six-node causal structure exhibits quantum correlations that cannot be reproduced classically, and they proved that such quantum correlations do exist, completing the classification for all causal structures with up to six nodes.
The discovery of Bell that there exist quantum correlations that cannot be reproduced classically is one of the most important in the foundations of quantum mechanics, as well as having practical implications. Bell's result was originally proven in a simple bipartite causal structure, but analogous results have also been shown in further causal structures. Here we study the only causal structure with six or fewer nodes in which the question of whether or not there exist quantum correlations that cannot be achieved classically was open. In this causal structure we show that such quantum correlations exist using a method that involves imposing additional restrictions on the correlations. This hence completes the picture of which causal structures of up to six nodes support non-classical quantum correlations. We also provide further illustrations of our method using other causal structures.