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. This description of the measuring process is a substantial generalization of current models in quantum measurement theory. In particular, 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 $\rho ).\mathrm{}$ A continuous limit of the above process leads to Lindblad’s equation for the quantum-dynamical semigroup [Commun. Math. Phys. $48,$ 119 (1976)].