A typical quantum measurement process involves two steps. Step one is to separate the initial wavefunction into its spatial components which are then guided towards detectors at different locations. The second step involves the direct detection of the particle by a detector. Such a measurement process presupposes the existence of an interaction which can produce step one. The authors give a general mathematical formulation of the first step and establish the existence of a unitary evolution group which produces the separation. The results obtained support the view that quantum measurements are reducible to local position measurements.