  Obtaining information from a quantum system through a measurement typically
disturbs its state. The postmeasurement states for a given measurement,
however, are not unique and highly rely on the chosen measurement model,
complicating the puzzle of information-disturbance. Two distinct questions are
then in order. Firstly, what is the minimum disturbance a measurement may
induce? Secondly, when a fixed disturbance occurs, how informative is the
possible measurement in the best-case scenario? Here, we propose various
approaches to tackle these questions and provide explicit solutions for the set
of unbiased binary qubit measurements and postmeasurement state spaces that are
equivalent to the image of a unital qubit channel. In particular, we show there
are different tradeoff relations between the sharpness of this measurement and
the average fidelity of the premeasurement and postmeasurement state spaces as
well as the sharpness and quantum resources preserved in the postmeasurement
states in terms of coherence and discord-like correlation once the measurement
is applied locally.
