  We study the noise properties and efficiency of a mesoscopic resonant-level
conductor which is used as a quantum detector, in the regime where transport
through the level is only partially phase coherent. We contrast models in which
detector incoherence arises from escape to a voltage probe, versus those in
which it arises from a random time-dependent potential. Particular attention is
paid to the back-action charge noise of the system. While the average detector
current is similar in all models, we find that its noise properties and
measurement efficiency are sensitive both to the degree of coherence and to the
nature of the dephasing source. Detector incoherence prevents quantum limited
detection, except in the non-generic case where the source of dephasing is not
associated with extra unobserved information. This latter case can be realized
in a version of the voltage probe model.
