  Every measurement on a quantum system causes a state change from the system
state just before the measurement to the system state just after the
measurement conditional upon the outcome of measurement. This paper determines
all the possible conditional state changes caused by measurements of
nondegenerate discrete observables. For this purpose, the following conditions
are shown to be equivalent for measurements of nondegenerate discrete
observables: (i) The joint probability distribution of the outcomes of
successive measurements depends affinely on the initial state. (ii) The
apparatus has an indirect measurement model. (iii) The state change is
described by a positive superoperator valued measure. (iv) The state change is
described by a completely positive superoperator valued measure. (v) The output
state is independent of the input state and the family of output states can be
arbitrarily chosen by the choice of the apparatus. The implications to the
measurement problem are discussed briefly.
