Guessing the outcome of separate and joint quantum measurements of noncommuting observables

According to Heisenberg's uncertainty relation, there is an ultimate limit how precisely we may predict the outcome of position and momentum measurements on a quantum system. We show that this be violated by arbitrarily large factor if one aims, instead, guess unknown value past measurement. For experiments single system, precise assignment measurement outcomes accompanied about their linear combinations, while entanglement with ancillary system permits accurate retrodiction any such combination. Finally, jointly measure multiple combinations observables means probe particles can also guessed no formal lower limit. present quantitative results for projective generalized where all components are prepared in Gaussian states.