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Bell's theorem states that Local Hidden Variables (LHVs) cannot fully explainthe statistics of measurements on some entangled quantum states. It is naturalto ask how much supplementary classical communication would be needed tosimulate them. We study two long-standing open questions in this field withneural network simulations and other tools. First, we present evidence that allprojective measurements on partially entangled pure two-qubit states requireonly one bit of communication. We quantify the statistical distance between theexact quantum behaviour and the product of the trained network, or of asemianalytical model inspired by it. Second, while it is known on generalgrounds (and obvious) that one bit of communication cannot eventually reproduceall bipartite quantum correlation, explicit examples have proved evasive. Oursearch failed to find one for several bipartite Bell scenarios with up to 5inputs and 4 outputs, highlighting the power of one bit of communication inreproducing quantum correlations.

Neural Network Approach to the Simulation of Entangled States with One Bit of Communication