Quantum stochastic calculus, operation valued stochastic processes, and continual measurements in quantum mechanics

The physical idea of a continual observation on a quantum system has been recently formalized by means of the concept of operation valued stochastic process (OVSP). In this article, it is shown how the formalism of quantum stochastic calculus of Hudson and Parthasarathy allows, in a simple way, for constructing a large class of OVSP’s that in particular contains the quantum counting processes of Davies and Srinivas and continual ‘‘Gaussian’’ measurements. This result is obtained by means of a stochastic dilation of the OVSP’s: at the level of the enlarged system probabilities turn out to be expressed in terms of projection valued measures associated with certain time-dependent, commuting, self-adjoint operators.