  A non-equilibrium theory describing the charge qubit dynamics measured by a
quantum point contact is developed based on Schwinger-Keldysh's approach. Using
the real-time diagram technique, we derive the master equation to all orders in
perturbation expansions. The non-Markovian processes in the qubit dynamics is
naturally taken into account. The qubit decoherence, in particular, the
influence of the tunneling-electron fluctuation in the quantum point contact
with a longer time correlation, is studied in the framework. We consider the
Lorentzian-type spectral density to characterize the channel mixture of the
electron tunneling processes induced by the measurement and determine the
correlation time scale of the tunneling-electron fluctuation. The result shows
that as the quantum point contact is casted with a narrower profile of the
spectral density, tunneling electrons can propagate with a longer time
correlation and lead to the non-Markovian processes of the qubit dynamics. The
qubit electron in the charge qubit will be driven coherently. The quantum point
contact measurement with the minimum deviation of the electron tunneling
processes prevents the qubit state from the decoherence.
