We start from the reasonable assumption that a quantum measurement can be properly described only when the measurement apparatus itself is also treated quantum mechanically. Using idealized optical measurements as an example and introducing a small loss into the measurement apparatus, we show that the combined density matrix of the system and apparatus decoheres in a manner that the outcome of the measurement can be described classically. The loss can be arbitrarily small when the classical limit of the measurement apparatus is taken, i.e., the gain is made to approach infinity. Further, we show that the von Neumann postulate of the collapse of the wave function of the measured system into an eigenstate of the measured observable can be deduced from the analysis of two quantum nondemolition experiments in cascade and need not be introduced as a separate postulate. © 1996 The American Physical Society.

• Received 29 September 1995

DOI:https://doi.org/10.1103/PhysRevA.53.3785