  In this thesis, I reflect on quantum instruments that measure the state of
pure finite dimensional quantum systems. As the Heisenberg principle dictates,
there exists a joint restriction to the information gain and distortion by
measurement of a quantum system. I minimize the distortion of measurement and
maximize the quality of the outcome by finding the optimal (covariant)
instrument. In order to optimize this joint restriction, the family of
covariant instruments is classified. This is an important side result.
