  When we extract information from a system by performing a quantum
measurement, the state of the system is disturbed due to the backaction of the
measurement. Numerous studies have been performed to quantitatively formulate
tradeoff relations between information and disturbance. We formulate a tradeoff
relation between information and disturbance from an estimation-theoretic point
of view, and derive an inequality between them. The information is defined as
the classical Fisher information obtained by the measurement, and the
disturbance is defined as the average loss of the quantum Fisher information.
We show that pure and reversible measurements achieve the equality of the
inequality. We also identify the necessary condition for various divergences
between two quantum states to satisfy a similar relation. The obtained relation
holds not only for the quantum relative entropy but also for the maximum
quantum relative entropy.
