UNITARY STATE PREPARATION, LOCAL POSITION MEASUREMENTS, AND SPIN IN QUANTUM-MECHANICS

The orthodox presentation of quantum theory often includes statements on state preparation and measurements without mentioning how these processes can be achieved. The often quoted projection postulate is regarded by many as problematical. This paper presents a systematic framework for state preparation and measurement. Within the existing Hilbert space formulation of quantum mechanics for spinless particles we show that it is possible (1) to prepare an arbitrary state and (2) to reduce all quantum measurements to local position measurements in an asymptotic way by unitary evolution processes without recourse to the projection postulate. A generalization to spin-1/2 particles is also given. The theory presented provides a general mathematical and theoretical foundation for many-practical schemes for state preparation and measurement.