  The possibility of determining the state of a quantum system after a
continuous measurement of position is discussed in the framework of quantum
trajectory theory. Initial lack of knowledge of the system and external noises
are accounted for by considering the evolution of conditioned density matrices
under a stochastic master equation. It is shown that after a finite time the
state of the system is a pure state and can be inferred from the measurement
record alone. The relation to emerging possibilities for the continuous
experimental observation of single quanta, as for example in cavity quantum
electrodynamics, is discussed.
