The theory of measurements continuous in time in quantum mechanics (quantum
continual measurements) has been formulated by using the notions of instrument,
positive operator valued measure, etc., by using quantum stochastic
differential equations and by using classical stochastic differential equations
(SDE's) for vectors in Hilbert spaces or for trace-class operators. In the same
times Ozawa made developments in the theory of instruments and introduced the
related notions of a posteriori states and of information gain [1].
In this paper we introduce a simple class of SDE's relevant to the theory of
continual measurements and we recall how they are related to instruments and a
posteriori states and, so, to the general formulation of quantum mechanics.
Then we introduce and use the notion of information gain and the other results
of the paper [1] inside the theory of continual measurements.
[1] M. Ozawa, On information gain by quantum measurements of continuous
observables, J. Math. Phys. 27 (1986) 759-763.Comment: 8 pages. Submitted to Proceedings of "Quantum Communication,
Computing, and Measurements (Capri, Italy, July 2000)
