Vectorial probability loophole in Bell test
Exhaustively identifying all loopholes in the Bell test is demanding for interpreting the results of the relevant experiments, since any loophole if not closed can be catastrophic to our understanding of the nonlocal structure of quantum mechanics. Despite a series of recent Bell experiments that claim to be free of loopholes, a united framework with a sound base is still missing to fully recognize all potential loopholes in these experiments, as verified by a recent experiment that has pinned down a detection loophole of a new type in Bell analysis. Here, we reveal another loophole previously unknown in the Bell test through a local theory developed here on the basis of a new mathematical concept of high-dimensional vectorial probability, quantified as a vector with interesting but hidden geometry in the probability space. We show that the statistical property of the stochastic events generated for the Bell test can be well described by the local theory, and, in particular, the correlations of these events that violate Bell's theorem can be closely connected to the geometry of the vectorial probability. To close the loophole, theoretical investigations are highly recommended to search for the statistical nature of the stochastic events in quantum measurements that can distinguish the predictions of quantum mechanics and those of the local theory.