Reciprocal ontological models show indeterminism of the order of quantum theory

The question whether indeterminism in quantum measurement outcomes is fundamental or is there a possibility of constructing a finer theory underlying quantum mechanics that allows no such indeterminism, has been debated for a long time. We show that within the class of ontological models due to Harrigan and Spekkens, those satisfying preparation-measurement reciprocity must allow indeterminism of the order of quantum theory. Our result implies that one can design quantum random number generator, for which it is impossible, even in principle, to construct a reciprocal deterministic model.