Noise and Measurement Efficiency of a Partially Coherent Mesoscopic Detector

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.