  We study generalized measurements (POVM measurements) on a single d-level
quantum system which is in a completely unknown pure state, and derive the best
estimate of the post-measurement state. The mean post-measuremement estimation
fidelity of a generalized measurement is obtained and related to the operation
fidelity of the device. This illustrates how the information gain about the
post-measurement state and the corresponding state disturbance are mutually
dependent. The connection between the best estimates of the pre- and
post-measurement state is established and interpreted. For pure generalized
measurements the two states coincide.
