Classical interventions in quantum systems. I. The measuring process

The measuring process is an external intervention in the dynamics of a quantum system. It involves a unitary interaction of that system with a measuring apparatus, a further interaction of both with an unknown environment causing decoherence, and then the deletion of a subsystem. No ancilla is needed. The final result is represented by a completely positive map of the quantum state $\rho$ (possibly with a change of the dimensions of $\rho$). A continuous limit of this process leads to the Lindblad equation.