A description of the measurement process by the parametric representation with environmental coherent states

We propose a description of the measurement process based on the parametric representation with environmental coherent states [1], where the environment is the measurement apparatus. Referring to the Von Neumann scheme, we first show that the premeasurement step induces a dynamical evolution for the density of environmental coherent states. The analysis of such evolution allows us to establish a formal relation between the loss of quantum coherence and the distinguishability of the measurement outputs. Moreover, having made use of generalized coherent states for the apparatus, we can consider the consequences of its being macroscopic referring to the relation between classical and large-N limit of a quantum theory, as established by G.Yaffe in Ref.[2]. This finally leads us to a statistical description of the actual production of the output that inherently includes both the probabilistic character of the process, with the Born rule properly recovered, and a symmetry breaking that entails the overall quantum state reduction. [1] Proceedings of the National Academy of Sciences 110, 6748-6753 (2013) [2] Rev. Mod. Phys. 54, 407 (1982)