  A sensitive technique for the readout of the state of a qubit is based on the
measurement of the conductance through a proximal sensor quantum dot (SQD).
Here, we theoretically study the coherent backaction of such a measurement on a
coupled SQD-charge-qubit system. We derive Markovian kinetic equations for the
ensemble-averaged state of the SQD-qubit system, expressed in the coupled
dynamics of two charge-state occupations of the SQD and two qubit isospin
vectors, one for each SQD charge state. We find that aside from introducing
dissipation, the detection also renormalizes the coherent evolution of the
SQD-qubit system. Basically, if the electron on the detector has time to probe
the qubit, then it also has time to fluctuate and thereby renormalize the
system parameters. In particular, this induces torques on the qubit isospins,
similar to the spin torque generated by the spintronic exchange field in
noncollinear spin-valve structures. Secondly, we show that for a consistent
description of the detection, one must also include the renormalization effects
in the next-to-leading order in the electron tunneling rates, especially at the
point of maximal sensitivity of the detector. Although we focus on a
charge-qubit model, our findings are generic for qubit readout schemes that are
based on spin-to-charge conversion using a quantum-dot detector. Furthermore,
our study of the stationary current through the SQD, a test measurement
verifying that the qubit couples to the detector current, already reveals
various significant effects of the isospin torques on the qubit. Our kinetic
equations provide a starting point for further studies of the time evolution in
charge-based qubit readout. Finally, we provide a rigorous sum rule that
constrains such approximate descriptions of the qubit isospin dynamics and show
that it is obeyed by our kinetic equations.
