  We consider the effect of electron-electron interactions on a voltage biased
quantum point contact in the tunneling regime used as a detector of a nearby
qubit. We model the leads of the quantum point contact as Luttinger liquids,
incorporate the effects of finite temperature and analyze the detection-induced
decoherence rate and the detector efficiency, $Q$. We find that interactions
generically reduce the induced decoherence along with the detector's
efficiency, and strongly affect the relative strength of the decoherence
induced by tunneling and that induced by interactions with the local density.
With increasing interaction strength, the regime of quantum-limited detection
($Q=1$) is shifted to increasingly lower temperatures or higher bias voltages
respectively. For small to moderate interaction strengths, $Q$ is a
monotonously decreasing function of temperature as in the non-interacting case.
Surprisingly, for sufficiently strong interactions we identify an intermediate
temperature regime where the efficiency of the detector increases with rising
temperature.
