Estimating the postmeasurement state

We study generalized measurements [positive-operator-valued measure (POVM measurements)] on a single d-level quantum system which is in a completely unknown pure state, and derive the best estimate of the postmeasurement state. The mean postmeasurement 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 postmeasurement state and the corresponding state disturbance are mutually dependent. The connection between the best estimates of the premeasurement and postmeasurement state is established and interpreted. For pure generalized measurements the two states coincide.