  It is not possible to obtain information about the observable properties of a
quantum system without a physical interaction between the system and an
external meter. This physical interaction is described by a unitary
transformation of the joint quantum state of the system and the meter, which
means that the information transfer from the system to the meter depends on the
initial quantum coherence of the meter. In the present paper, we analyze the
measurement interaction in terms of the changes of the meter state caused by
the interaction with the system. The sensitivity of the meter can then be
defined by evaluating the distinguishability of meter states for different
values of the target observable. It is shown that the sensitivity of the meter
requires quantum coherences in the generator observable that determines the
magnitude of the back action of the meter on the system. The trade-off between
measurement resolution and back action is decided by the relation between
sensitivity and quantum coherent uncertainty in the external meter. No matter
how macroscopic the device used as a meter is, it must necessarily be quantum
coherent in the degrees of freedom that interact with the system being
measured.
