  Every measurement leaves the object in a family of states indexed by the
possible outcomes. This family, called the posterior states, is usually a
family of the eigenstates of the measured observable, but it can be an
arbitrary family of states by controlling the object-apparatus interaction. A
potentially realizable object-apparatus interaction measures position in such a
way that the posterior states are the translations of an arbitrary wave
function. In particular, position can be measured without perturbing the object
in a momentum eigenstate.
