Disproving Heisenberg’s error-disturbance relation

Recently, Busch, Lahti, and Werner [1] claimed that Heisenberg’s error-disturbance relation can be proved in its original form with new formulations of error and disturbance, in contrast to the theory proposed by the present author [2–5] and confirmed by recent experiments [6–9]. Despite their claim, it is shown here that a class of solvable models of position measurement with explicit interaction Hamiltonians escape the Busch-Lahti-Werner relation. It is also made clear where their proof fails. Those models have unambiguously defined zero root-mean-square error and finite rootmean-square disturbance in every input state and are naturally considered to violate Heisenberg’s error-disturbance relation in any conceivable formulation.