Getting information via a quantum measurement: the role of decoherence

Abstract: 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, referring to the Von Neumann scheme for ideal quantum measurements, we first look for the minimal structure that the interaction between principal system and measurement apparatus must have for properly describing the process, beyond the quantum measurement limit, and then analyze the dynamical evolution induced by one such interaction. The analysis is developed by means of a recently introduced method for studying open quantum systems, namely the parametric representation with environmental coherent states, that allows us to determine a necessary condition that the quantum state of the apparatus must fullfil in order to give information on the observable being measured. We find that this condition strictly implies decoherence in the principal system, with respect to the eigenstates of the hermitian operator that represents the measured observable, thus establishing that there cannot be information flux from a quantum system towards a readable analyser unless decoherence occurs. The relevance of dynamical entanglement generation is highlighted, and consequences of the possible macroscopic structure of the measurement apparatus are also commented upon.