Abstract
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.
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