  We propose a generalisation of the Leggett-Garg conditions for macrorealistic
behaviour. Our proposal relies on relaxing the postulate of non-invasive
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 optimise over all possible state updates, for
retrievability of information it suffices to use the basic L\"uders 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 generalisation of
macrorealism.
