Decay of quantumness in a measurement process: Action of a coarse-graining channel

A model of a quantum measurement process is presented: a system consisting of a qubit in a superposition interacts with a measuring apparatus consisting of a N qubit state. Looking at the emerging, effective description of the apparatus given by the action of a coarse-graining channel, we have been able to recover information about the superposition coefficients of the system.We have also been able to visualize the death of quantum correlations between system and apparatus and the death of quantum coherences in the apparatus’ effective state, in the limit of a strong coarse-graining action - a situation akin to decoherence, although it is not necessary to evoke any interaction with the surrounding environment.