Getting Information via a quantum measurement: the role of decoherence

In this work we investigate the relation between quantum measurements and decoherence, in order to formally express the necessity of the latter for obtaining an informative output from the former. To this aim, we analyse the dynamical behaviour of a particular model, which is often adopted in the literature for describing projector valued measures of discrete observables. The analysis is developed by a recently introduced method for studying open quantum systems, namely the parametric representation with environmental coherent states: this method allows us to determine a necessary condition that the evolved quantum state of the apparatus must fulfil in order to have the properties that a measurement scheme requests it to feature. We find that this condition strictly implies decoherence in the system object of the measurement, with respect to the eigenstates of the hermitian operator that represents the measured observable. The relevance of dynamical entanglement generation is highlighted, and consequences of the possible macroscopic structure of the measurement apparatus are also commented upon.