Approximate measurement in quantum mechanics. II

An approximate measurement procedure of the following type is considered: (i) An initial eigenstate of the object observable leads to a final statistical operator of the object plus apparatus describing a mixture of exact eigenstates of the apparatus observable; (ii) almost all the statistical weight of the mixture is assigned to eigenstates associated with one eigenvalue of the apparatus observable, which is uniquely determined by the initial value of the object observable. It is proved that each of a large class of initial states of the object leads to a final statistical operator which does not describe any mixture of exact eigenstates of the apparatus observable. The analysis also yields a proof of a theorem on measurement stated by Fine.