Retrievability of information in quantum and realistic hidden-variable theories

We propose a generalization of the Leggett-Garg conditions for macrorealistic behavior. Our proposal relies on relaxing the postulate of noninvasive measurability with that of retrievability of information. This leads to a strictly broader class of hidden-variable theories than those having a macrorealistic description. Crucially, whereas quantum mechanical tests of macrorealism require one to optimize over all possible state updates, for retrievability of information it suffices to use the basic L & uuml;ders state update, which is present in every quantum measurement. We show that in qubit systems the optimal retrieving protocols further relate to the fundamental precision limit of quantum theory given by Busch-Lahti-Werner error-disturbance uncertainty relations. We implement an optimal protocol using a photonic setting and report an experimental violation of the proposed generalization of macrorealism.