Characterising quantum non-locality using simple physical principles has become a hot topic in quantum foundations of late. In the simpler case of local hidden variable models, the space of allowed correlations can be characterised by requiring that there exists a joint probability distribution over all possible experimental outcomes, from which the experimental probabilities arise as marginals. This follows from Bell’s causality condition. But the existing characterisations of quantum correlations are far from being so straightforward.
Motivated by a histories outlook, we propose the following condition: there exists a positive semi-definite matrix in which the indices run over all possible experimental outcomes, from which the experimental probabilities arise as “marginals” in a similar way. This is a much simpler condition than the usual statement of the existence of a quantum model for the probabilities, and suggests an underlying connection with Bell’s derivation of his bound on local correlations. I will outline existing proofs that this condition places strong bounds on correlations consistent with QM, and ask whether it could completely characterise quantum non-locality