Quantum limit of measurement and the projection postulate

We study an electrostatic qubit monitored by a point-contact detector. Projecting an entire qubit-detector wave function on the detector eigenstates we determine the precision limit for the qubit measurements, allowed by quantum mechanics. We found that this quantity is determined by qubit dynamics as well as decoherence, generated by the measurement. Our results show how the quantum precision limit can be improved by a proper design of a measurement procedure.